diff --git a/pdm.lock b/pdm.lock
index 6c740e0..a2790db 100644
--- a/pdm.lock
+++ b/pdm.lock
@@ -3,62 +3,63 @@
 
 [metadata]
 groups = ["default", "dev"]
-cross_platform = true
-static_urls = false
-lock_version = "4.3"
-content_hash = "sha256:1ea2a67b922f09a5ea095570a9484ea9b1ce6de9e6f15504614a2c77d17870f3"
+strategy = []
+lock_version = "4.5.0"
+content_hash = "sha256:6b25edceb64e0f136ece2dec1ba538d01835dfe63a0db6e2d085fe65f8dfb63f"
+
+[[metadata.targets]]
+requires_python = ">=3.10,<3.13"
 
 [[package]]
 name = "absl-py"
-version = "1.4.0"
-requires_python = ">=3.6"
+version = "2.1.0"
+requires_python = ">=3.7"
 summary = "Abseil Python Common Libraries, see https://github.com/abseil/abseil-py."
 files = [
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+    {file = "absl-py-2.1.0.tar.gz", hash = "sha256:7820790efbb316739cde8b4e19357243fc3608a152024288513dd968d7d959ff"},
+    {file = "absl_py-2.1.0-py3-none-any.whl", hash = "sha256:526a04eadab8b4ee719ce68f204172ead1027549089702d99b9059f129ff1308"},
 ]
 
 [[package]]
 name = "appnope"
-version = "0.1.3"
+version = "0.1.4"
+requires_python = ">=3.6"
 summary = "Disable App Nap on macOS >= 10.9"
 files = [
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 ]
 
 [[package]]
 name = "arviz"
-version = "0.15.1"
-requires_python = ">=3.8"
+version = "0.20.0"
+requires_python = ">=3.10"
 summary = "Exploratory analysis of Bayesian models"
 dependencies = [
     "h5netcdf>=1.0.2",
-    "matplotlib>=3.2",
-    "numpy>=1.20.0",
+    "matplotlib>=3.5",
+    "numpy>=1.23.0",
     "packaging",
-    "pandas>=1.3.0",
-    "scipy>=1.8.0",
+    "pandas>=1.5.0",
+    "scipy>=1.9.0",
     "setuptools>=60.0.0",
     "typing-extensions>=4.1.0",
     "xarray-einstats>=0.3",
-    "xarray>=0.21.0",
+    "xarray>=2022.6.0",
 ]
 files = [
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 ]
 
 [[package]]
 name = "asttokens"
-version = "2.2.1"
+version = "3.0.0"
+requires_python = ">=3.8"
 summary = "Annotate AST trees with source code positions"
-dependencies = [
-    "six",
-]
 files = [
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 [[package]]
@@ -76,27 +77,18 @@ files = [
 
 [[package]]
 name = "attrs"
-version = "23.1.0"
-requires_python = ">=3.7"
+version = "24.3.0"
+requires_python = ">=3.8"
 summary = "Classes Without Boilerplate"
 files = [
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-
-[[package]]
-name = "backcall"
-version = "0.2.0"
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 [[package]]
 name = "black"
-version = "23.7.0"
-requires_python = ">=3.8"
+version = "24.10.0"
+requires_python = ">=3.9"
 summary = "The uncompromising code formatter."
 dependencies = [
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 [[package]]
 name = "cachetools"
-version = "5.3.1"
+version = "5.5.0"
 requires_python = ">=3.7"
 summary = "Extensible memoizing collections and decorators"
 files = [
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 [[package]]
 name = "certifi"
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 requires_python = ">=3.6"
 summary = "Python package for providing Mozilla's CA Bundle."
 files = [
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 name = "cffi"
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 summary = "Foreign Function Interface for Python calling C code."
 dependencies = [
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 [[package]]
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+version = "8.1.7"
 requires_python = ">=3.7"
 summary = "Composable command line interface toolkit"
 dependencies = [
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-requires_python = ">=3.6"
-summary = "Extended pickling support for Python objects"
+version = "3.1.0"
+requires_python = ">=3.8"
+summary = "Pickler class to extend the standard pickle.Pickler functionality"
 files = [
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 [[package]]
@@ -322,15 +288,15 @@ files = [
 
 [[package]]
 name = "comm"
-version = "0.1.4"
-requires_python = ">=3.6"
+version = "0.2.2"
+requires_python = ">=3.8"
 summary = "Jupyter Python Comm implementation, for usage in ipykernel, xeus-python etc."
 dependencies = [
     "traitlets>=4",
 ]
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 ]
 
 [[package]]
 name = "xarray"
-version = "2023.1.0"
-requires_python = ">=3.8"
+version = "2024.11.0"
+requires_python = ">=3.10"
 summary = "N-D labeled arrays and datasets in Python"
 dependencies = [
-    "numpy>=1.20",
-    "packaging>=21.3",
-    "pandas>=1.3",
+    "numpy>=1.24",
+    "packaging>=23.2",
+    "pandas>=2.1",
 ]
 files = [
-    {file = "xarray-2023.1.0-py3-none-any.whl", hash = "sha256:7e530b1deafdd43e5c2b577d0944e6b528fbe88045fd849e49a8d11871ecd522"},
-    {file = "xarray-2023.1.0.tar.gz", hash = "sha256:7bee552751ff1b29dab8b7715726e5ecb56691ac54593cf4881dff41978ce0cd"},
+    {file = "xarray-2024.11.0-py3-none-any.whl", hash = "sha256:6ee94f63ddcbdd0cf3909d1177f78cdac756640279c0e32ae36819a89cdaba37"},
+    {file = "xarray-2024.11.0.tar.gz", hash = "sha256:1ccace44573ddb862e210ad3ec204210654d2c750bec11bbe7d842dfc298591f"},
 ]
 
 [[package]]
 name = "xarray-einstats"
-version = "0.5.1"
-requires_python = ">=3.8"
+version = "0.8.0"
+requires_python = ">=3.10"
 summary = "Stats, linear algebra and einops for xarray"
 dependencies = [
-    "numpy>=1.20",
-    "scipy>=1.6",
+    "numpy>=1.23",
+    "scipy>=1.9",
     "xarray>=2022.09.0",
 ]
 files = [
-    {file = "xarray-einstats-0.5.1.tar.gz", hash = "sha256:45283e8b471ac54ac2957bc14e311f681b84dabc50c85959b9931e6f5cc60bcb"},
-    {file = "xarray_einstats-0.5.1-py3-none-any.whl", hash = "sha256:cfe63d788077b667624c96d0b0a9144323861888a4d519777083234929b0de2d"},
+    {file = "xarray_einstats-0.8.0-py3-none-any.whl", hash = "sha256:fd00552c3fb5c859b1ebc7c88a97342d3bb93d14bba904c5a9b94a4f724b76b4"},
+    {file = "xarray_einstats-0.8.0.tar.gz", hash = "sha256:7f1573f9bd4d60d6e7ed9fd27c4db39da51ec49bf8ba654d4602a139a6309d7f"},
 ]
 
 [[package]]
-name = "zipp"
-version = "3.16.2"
-requires_python = ">=3.8"
-summary = "Backport of pathlib-compatible object wrapper for zip files"
+name = "zuko"
+version = "1.3.1"
+requires_python = ">=3.9"
+summary = "Normalizing flows in PyTorch"
+dependencies = [
+    "numpy>=1.20.0",
+    "torch>=1.12.0",
+]
 files = [
-    {file = "zipp-3.16.2-py3-none-any.whl", hash = "sha256:679e51dd4403591b2d6838a48de3d283f3d188412a9782faadf845f298736ba0"},
-    {file = "zipp-3.16.2.tar.gz", hash = "sha256:ebc15946aa78bd63458992fc81ec3b6f7b1e92d51c35e6de1c3804e73b799147"},
+    {file = "zuko-1.3.1-py3-none-any.whl", hash = "sha256:35865355f273e109cd32df2d41c24271349833c4bedf34a7f3870e2872274421"},
+    {file = "zuko-1.3.1.tar.gz", hash = "sha256:00f246802d3f486183185529ba22e0b2bf691397e03b28150a5cf713fa0da758"},
 ]
diff --git a/pyproject.toml b/pyproject.toml
index 2c68d85..ed5c657 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -11,7 +11,7 @@ name = "bayesian_inference"
 description = "Analysis pipeline to implement Bayesian inference in high-energy physics "
 license = {text = "BSD-3-Clause"}
 # NOTE: <3.12 cap needed for tensorflow-io-gcs-filesystem
-requires-python = ">=3.8,<3.12"
+requires-python = ">=3.10,<3.13"
 authors = [
   { name = "James Mulligan", email = "james.mulligan@berkeley.edu" },
   { name = "Raymond Ehlers", email = "raymond.ehlers@cern.ch" },
@@ -36,15 +36,15 @@ dependencies = [
     "statsmodels>=0.14.0",
 ]
 
-# NOTE: If moving to hatch, move this to "[project.optional-dependencies]"
-[tool.pdm.dev-dependencies]
+[project.optional-dependencies]
 dev = [
-    "ruff>=0.0.209",
+    "ruff >=0.0.209",
     "black >=22.1.0",
     "mypy >=0.931",
     "ipython >=8.0",
     "ipykernel >=6.15.1",
-    "pytest>=7.4.0",
+    "pytest >=7.4.0",
+    "pocoMC >=1.2.2",
 ]
 
 [tool.hatch]
@@ -56,6 +56,28 @@ version = { source = "file", path = "src/bayesian_inference/__init__.py" }
 [tool.black]
 line-length = 120
 
+[tool.mypy]
+files = ["src", "tests"]
+python_version = "3.10"
+warn_unused_configs = true
+strict = true
+show_error_codes = true
+enable_error_code = ["ignore-without-code", "redundant-expr", "truthy-bool"]
+warn_unreachable = true
+no_implicit_reexport = false
+disallow_untyped_defs = false
+disallow_incomplete_defs = false
+exclude = [".venv*"]
+
+[[tool.mypy.overrides]]
+module = [
+    "sklearn",
+    "sklearn.decompoistion",
+    "sklearn.gaussian_process",
+    "sklearn.preprocessing",
+]
+ignore_missing_imports = true
+
 [tool.ruff]
 exclude = [
     '.git',
diff --git a/src/bayesian_inference/emulation.py b/src/bayesian_inference/emulation.py
index 5f82c74..df8559a 100644
--- a/src/bayesian_inference/emulation.py
+++ b/src/bayesian_inference/emulation.py
@@ -1,4 +1,3 @@
-#! /usr/bin/env python
 '''
 Module related to emulators, with functionality to train and call emulators for a given analysis run
 
@@ -16,20 +15,19 @@
 
 import logging
 import os
-import yaml
+import pickle
 from pathlib import Path
 from typing import Any
 
 import attrs
 import numpy as np
 import numpy.typing as npt
-import pickle
-import sklearn.preprocessing as sklearn_preprocessing
 import sklearn.decomposition as sklearn_decomposition
 import sklearn.gaussian_process as sklearn_gaussian_process
+import sklearn.preprocessing as sklearn_preprocessing
+import yaml
 
-from bayesian_inference import data_IO
-from bayesian_inference import common_base
+from bayesian_inference import common_base, data_IO
 
 logger = logging.getLogger(__name__)
 
@@ -61,9 +59,9 @@ def fit_emulator_group(config: EmulationGroupConfig) -> dict[str, Any]:
     '''
 
     # Check if emulator already exists
-    if os.path.exists(config.emulation_outputfile):
+    if config.emulation_outputfile.exists():
         if config.force_retrain:
-            os.remove(config.emulation_outputfile)
+            config.emulation_outputfile.unlink()
             logger.info(f'Removed {config.emulation_outputfile}')
         else:
             logger.info(f'Emulators already exist: {config.emulation_outputfile} (to force retrain, set force_retrain: True)')
@@ -72,7 +70,7 @@ def fit_emulator_group(config: EmulationGroupConfig) -> dict[str, Any]:
     # Initialize predictions into a single 2D array: (design_point_index, observable_bins) i.e. (n_samples, n_features)
     # A consistent order of observables is enforced internally in data_IO
     # NOTE: One sample corresponds to one design point, while one feature is one bin of one observable
-    logger.info(f'Doing PCA...')
+    logger.info('Doing PCA...')
     Y = data_IO.predictions_matrix_from_h5(config.output_dir, filename=config.observables_filename, observable_filter=config.observable_filter)
 
     # Use sklearn to:
@@ -112,6 +110,8 @@ def fit_emulator_group(config: EmulationGroupConfig) -> dict[str, Any]:
     max_n_components = config.max_n_components_to_calculate
     if max_n_components is not None:
         logger.info(f"Running with max n_pc={max_n_components}")
+    # NOTE-STAT: Whiten=True, but here, Whiten=False.
+    # NOTE-STAT: RJE thinks this doesn't matter, based on the comments above.
     pca = sklearn_decomposition.PCA(n_components=max_n_components, svd_solver='full', whiten=False) # Include all PCs here, so we can access them later
     # Scale data and perform PCA
     Y_pca = pca.fit_transform(scaler.fit_transform(Y))
@@ -164,7 +164,7 @@ def fit_emulator_group(config: EmulationGroupConfig) -> dict[str, Any]:
     # Fit a GP (optimize the kernel hyperparameters) to map each design point to each of its PCs
     # Note that Y_PCA=(n_samples, n_components), so each PC corresponds to a row (i.e. a column of Y_PCA.T)
     logger.info("")
-    logger.info(f'Fitting GPs...')
+    logger.info('Fitting GPs...')
     logger.info(f'  The design has {design.shape[1]} parameters')
     emulators = [sklearn_gaussian_process.GaussianProcessRegressor(kernel=kernel,
                                                              alpha=config.alpha,
@@ -199,7 +199,8 @@ def read_emulators(config: EmulationGroupConfig) -> dict[str, Any]:
 
     with filename.open("rb") as f:
         results = pickle.load(f)
-    return results
+    return results  # noqa: RET504
+
 
 ####################################################################################################################
 def write_emulators(config: EmulationGroupConfig, output_dict: dict[str, Any]) -> None:
@@ -208,10 +209,11 @@ def write_emulators(config: EmulationGroupConfig, output_dict: dict[str, Any]) -
     filename = Path(config.emulation_outputfile)
 
     with filename.open('wb') as f:
-	    pickle.dump(output_dict, f)
+        pickle.dump(output_dict, f)
+
 
 ####################################################################################################################
-def compute_emulator_cov_unexplained(emulation_config, emulation_results):
+def compute_emulator_cov_unexplained(emulation_config, emulation_results) -> dict:
     '''
     Compute the predictive variance due to PC truncation, for all emulator groups.
     See further details in compute_emulator_group_cov_unexplained().
@@ -222,6 +224,8 @@ def compute_emulator_cov_unexplained(emulation_config, emulation_results):
     for emulation_group_name, emulation_group_config in emulation_config.emulation_groups_config.items():
         emulation_group_result = emulation_results.get(emulation_group_name)
         emulator_cov_unexplained[emulation_group_name] = compute_emulator_group_cov_unexplained(emulation_group_config, emulation_group_result)
+    return emulator_cov_unexplained
+
 
 ####################################################################################################################
 def compute_emulator_group_cov_unexplained(emulation_group_config, emulation_group_result):
@@ -243,12 +247,15 @@ def compute_emulator_group_cov_unexplained(emulation_group_config, emulation_gro
     We will generally pre-compute this once in mcmc.py to save time, although we define this function
     here to allow us to re-compute it as needed if it is not pre-computed (e.g. when plotting).
     '''
+    # TODO: NOTE-STAT: Compare this more carefully with STAT L145 and on.
     pca = emulation_group_result['PCA']['pca']
     S_unexplained = pca.components_.T[:,emulation_group_config.n_pc:]
     D_unexplained = np.diag(pca.explained_variance_[emulation_group_config.n_pc:])
     emulator_cov_unexplained = S_unexplained.dot(D_unexplained.dot(S_unexplained.T))
 
-    return emulator_cov_unexplained
+    # NOTE-STAT: bayesian-inference does not include a small term for numerical stability
+    return emulator_cov_unexplained  # noqa: RET504
+
 
 ####################################################################################################################
 def nd_block_diag(arrays):
@@ -351,7 +358,7 @@ def convert(self, group_matrices: dict[str, dict[str, npt.NDArray[np.float64]]])
         :return: Converted matrix for each available value type.
         """
         if self._available_value_types is None:
-            self._available_value_types = set([
+            self._available_value_types = set([  # noqa: C403
                 value_type
                 for group in group_matrices.values()
                 for value_type in group
@@ -443,9 +450,9 @@ def predict(parameters: npt.NDArray[np.float64],
 
         # Compute unexplained variance due to PC truncation for this emulator group, if not already precomputed
         if emulator_cov_unexplained:
-            emulator_group_cov_unexplained=emulator_cov_unexplained[emulation_group_name]
+            emulator_group_cov_unexplained = emulator_cov_unexplained[emulation_group_name]
         else:
-            emulator_group_cov_unexplained=compute_emulator_group_cov_unexplained(emulation_group_config, emulation_group_result)
+            emulator_group_cov_unexplained = compute_emulator_group_cov_unexplained(emulation_group_config, emulation_group_result)
 
         predict_output[emulation_group_name] = predict_emulation_group(
             parameters,
@@ -519,6 +526,7 @@ def predict_emulation_group(parameters, results, emulation_group_config, emulato
     # So C_Y[i] = S * C_Y_PCA[i] * S^T.
     # Note: should be equivalent to: https://github.com/jdmulligan/STAT/blob/master/src/emulator.py#L145
     # TODO: one can make this faster with broadcasting/einsum
+    # TODO: NOTE-STAT: Compare this more carefully with STAT L286 and on.
     n_features = pca.components_.shape[1]
     S = pca.components_.T[:,:emulation_group_config.n_pc]
     emulator_cov_reconstructed_scaled = np.zeros((n_samples, n_features, n_features))
@@ -560,7 +568,7 @@ def __init__(self, analysis_name='', parameterization='', analysis_config='', co
         self.analysis_config = analysis_config
         self.config_file = config_file
 
-        with open(self.config_file, 'r') as stream:
+        with open(self.config_file) as stream:
             config = yaml.safe_load(stream)
 
         # Observable inputs
@@ -591,13 +599,14 @@ def __init__(self, analysis_name='', parameterization='', analysis_config='', co
         # Validation for noise configuration
         if 'noise' in self.active_kernels:
             # Check we have the appropriate keys
-            assert [k in self.active_kernels['noise'].keys() for k in ["type", "args"]], "Noise configuration must have keys 'type' and 'args'"
+            assert [k in self.active_kernels['noise'] for k in ["type", "args"]], "Noise configuration must have keys 'type' and 'args'"
             if self.active_kernels['noise']["type"] == "white":
                 # Validate arguments
                 # We don't want to do too much since we'll just be reinventing the wheel, but a bit can be helpful.
-                assert set(self.active_kernels['noise']["args"]) == set(["noise_level", "noise_level_bounds"]), "Must provide arguments 'noise_level' and 'noise_level_bounds' for white noise kernel"
+                assert set(self.active_kernels['noise']["args"]) == set(["noise_level", "noise_level_bounds"]), "Must provide arguments 'noise_level' and 'noise_level_bounds' for white noise kernel"  # noqa: C405
             else:
-                raise ValueError("Unsupported noise kernel")
+                msg = "Unsupported noise kernel"
+                raise ValueError(msg)
 
         # GPR
         self.n_restarts = emulator_configuration["GPR"]['n_restarts']
@@ -615,11 +624,11 @@ def __init__(self, analysis_name='', parameterization='', analysis_config='', co
             )
 
         # Output options
-        self.output_dir = os.path.join(config['output_dir'], f'{analysis_name}_{parameterization}')
+        self.output_dir = Path(config['output_dir']) / f'{analysis_name}_{parameterization}'
         emulation_outputfile_name = 'emulation.pkl'
         if emulation_group_name is not None:
             emulation_outputfile_name = f'emulation_group_{emulation_group_name}.pkl'
-        self.emulation_outputfile = os.path.join(self.output_dir, emulation_outputfile_name)
+        self.emulation_outputfile = Path(self.output_dir) /  emulation_outputfile_name
 
 @attrs.define
 class EmulationConfig(common_base.CommonBase):
@@ -685,7 +694,8 @@ def read_all_emulator_groups(self) -> dict[str, dict[str, npt.NDArray[np.float64
     def observable_filter(self) -> data_IO.ObservableFilter:
         if self._observable_filter is None:
             if not self.emulation_groups_config:
-                raise ValueError("Need to specify emulation groups to provide an observable filter")
+                msg = "Need to specify emulation groups to provide an observable filter"
+                raise ValueError(msg)
             # Accumulate the include and exclude lists from all emulation groups
             include_list: list[str] = []
             exclude_list: list[str] = self.config.get("global_observable_exclude_list", [])
@@ -703,7 +713,8 @@ def observable_filter(self) -> data_IO.ObservableFilter:
     def sort_observables_in_matrix(self) -> SortEmulationGroupObservables:
         if self._sort_observables_in_matrix is None:
             if not self.emulation_groups_config:
-                raise ValueError("Need to specify emulation groups to provide an sorting for observable group observables")
+                msg = "Need to specify emulation groups to provide an sorting for observable group observables"
+                raise ValueError(msg)
             # Accumulate the include and exclude lists from all emulation groups
             self._sort_observables_in_matrix = SortEmulationGroupObservables.learn_mapping(self)
-        return self._sort_observables_in_matrix
\ No newline at end of file
+        return self._sort_observables_in_matrix
diff --git a/src/bayesian_inference/log_posterior.py b/src/bayesian_inference/log_posterior.py
index 135b104..d61f5a9 100644
--- a/src/bayesian_inference/log_posterior.py
+++ b/src/bayesian_inference/log_posterior.py
@@ -1,14 +1,17 @@
 """Define the likelihood separately for performance reasons
 
-In doing so, we can use global variables. This isn't a nice thing to do, but it may improve MCMC performance
-during multiprocessing.
-
+In doing so, we can use global variables. This isn't a nice thing to do from a coding perspective,
+but it gives a significant improvement in MCMC performance during multiprocessing.
+For the initial concept, see: https://emcee.readthedocs.io/en/stable/tutorials/parallel/#parallel
 
+.. codeauthor:: Raymond Ehlers <raymond.ehlers@cern.ch>, LBL/UCB
+.. codeauthor:: James Mulligan
 """
 
 import logging
 
 import numpy as np
+import numpy.typing as npt
 from scipy.linalg import lapack
 
 from bayesian_inference import emulation
@@ -16,30 +19,30 @@
 logger = logging.getLogger(__name__)
 
 
-min = None
-max = None
-emulation_config = None
-emulation_results = None
-experimental_results = None
-emulator_cov_unexplained = None
+g_min: npt.NDArray[np.float64] = None
+g_max: npt.NDArray[np.float64] = None
+g_emulation_config: emulation.EmulationConfig = None
+g_emulation_results: dict[str, dict[str, npt.NDArray[np.float64]]] = None
+g_experimental_results: dict = None
+g_emulator_cov_unexplained: dict = None
 
 def initialize_pool_variables(local_min, local_max, local_emulation_config, local_emulation_results, local_experimental_results, local_emulator_cov_unexplained) -> None:
-    global min 
-    global max
-    global emulation_config
-    global emulation_results
-    global experimental_results
-    global emulator_cov_unexplained
-    min = local_min
-    max = local_max
-    emulation_config = local_emulation_config
-    emulation_results = local_emulation_results
-    experimental_results = local_experimental_results
-    emulator_cov_unexplained = local_emulator_cov_unexplained
+    global g_min  # noqa: PLW0603
+    global g_max  # noqa: PLW0603
+    global g_emulation_config  # noqa: PLW0603
+    global g_emulation_results  # noqa: PLW0603
+    global g_experimental_results  # noqa: PLW0603
+    global g_emulator_cov_unexplained  # noqa: PLW0603
+    g_min = local_min
+    g_max = local_max
+    g_emulation_config = local_emulation_config
+    g_emulation_results = local_emulation_results
+    g_experimental_results = local_experimental_results
+    g_emulator_cov_unexplained = local_emulator_cov_unexplained
 
 
 #---------------------------------------------------------------
-def log_posterior(X):
+def log_posterior(X, *, set_to_infinite_outside_bounds: bool = True) -> npt.NDArray[np.float64]:
     """
     Function to evaluate the log-posterior for a given set of input parameters.
 
@@ -60,26 +63,27 @@ def log_posterior(X):
     log_posterior = np.zeros(X.shape[0])
 
     # Check if any samples are outside the parameter bounds, and set log-posterior to -inf for those
-    inside = np.all((X > min) & (X < max), axis=1)
-    log_posterior[~inside] = -np.inf
+    inside = np.all((X > g_min) & (X < g_max), axis=1)  # noqa: SIM300
+    # -1e300 is apparently preferred for pocoMC
+    log_posterior[~inside] = -np.inf if set_to_infinite_outside_bounds else -1e300
 
     # Evaluate log-posterior for samples inside parameter bounds
     n_samples = np.count_nonzero(inside)
-    n_features = experimental_results['y'].shape[0]
+    n_features = g_experimental_results['y'].shape[0]
 
     if n_samples > 0:
 
         # Get experimental data
-        data_y = experimental_results['y']
-        data_y_err = experimental_results['y_err']
+        data_y = g_experimental_results['y']
+        data_y_err = g_experimental_results['y_err']
 
         # Compute emulator prediction
         # Returns dict of matrices of emulator predictions:
         #     emulator_predictions['central_value'] -- (n_samples, n_features)
         #     emulator_predictions['cov'] -- (n_samples, n_features, n_features)
-        emulator_predictions = emulation.predict(X[inside], emulation_config, 
-                                                 emulation_group_results=emulation_results,
-                                                 emulator_cov_unexplained=emulator_cov_unexplained)
+        emulator_predictions = emulation.predict(X[inside], g_emulation_config,
+                                                 emulation_group_results=g_emulation_results,
+                                                 emulator_cov_unexplained=g_emulator_cov_unexplained)
 
         # Construct array to store the difference between emulator prediction and experimental data
         # (using broadcasting to subtract each data point from each emulator prediction)
@@ -87,7 +91,7 @@ def log_posterior(X):
         dY = emulator_predictions['central_value'] - data_y
 
         # Construct the covariance matrix
-        # TODO: include full experimental data covariance matrix -- currently we only include uncorrelated data uncertainty
+        # NOTE-STAT TODO: include full experimental data covariance matrix -- currently we only include uncorrelated data uncertainty
         #-------------------------
         covariance_matrix = np.zeros((n_samples, n_features, n_features))
         covariance_matrix += emulator_predictions['cov']
@@ -98,6 +102,8 @@ def log_posterior(X):
         # (since above we set the log-posterior to -inf for samples outside the parameter bounds)
         log_posterior[inside] += list(map(_loglikelihood, dY, covariance_matrix))
 
+        # NOTE-STAT: We don't support the extra_std term here.
+
     return log_posterior
 
 #---------------------------------------------------------------
@@ -123,24 +129,21 @@ def _loglikelihood(y, cov):
     L, info = lapack.dpotrf(cov, clean=False)
 
     if info < 0:
-        raise ValueError(
-            'lapack dpotrf error: '
-            'the {}-th argument had an illegal value'.format(-info)
-        )
-    elif info < 0:
-        raise np.linalg.LinAlgError(
-            'lapack dpotrf error: '
-            'the leading minor of order {} is not positive definite'
-            .format(info)
-        )
+        msg = 'lapack dpotrf error: '
+        msg += f'the {-info}-th argument had an illegal value'
+        raise ValueError(msg)
+    if info < 0:
+        msg = 'lapack dpotrf error: '
+        msg += f'the leading minor of order {info} is not positive definite'
+        raise np.linalg.LinAlgError(msg)
 
     # Solve for alpha = cov^-1.y using the Cholesky decomp.
     alpha, info = lapack.dpotrs(L, y)
 
     if info != 0:
+        msg = 'lapack dpotrs error: '
+        msg += f'the {-info}-th argument had an illegal value'
         raise ValueError(
-            'lapack dpotrs error: '
-            'the {}-th argument had an illegal value'.format(-info)
         )
 
     return -.5*np.dot(y, alpha) - np.log(L.diagonal()).sum()
diff --git a/src/bayesian_inference/mcmc.py b/src/bayesian_inference/mcmc.py
index 583c5bc..01f69c8 100644
--- a/src/bayesian_inference/mcmc.py
+++ b/src/bayesian_inference/mcmc.py
@@ -1,4 +1,3 @@
-#! /usr/bin/env python
 '''
 Module related to MCMC, with functionality to compute posterior for a given analysis run
 
@@ -11,33 +10,28 @@
 authors: J.Mulligan, R.Ehlers
 Based in part on JETSCAPE/STAT code.
 '''
+from __future__ import annotations
 
-import os
-import yaml
 import logging
-import os
+import multiprocessing
 import pickle
+from pathlib import Path
 
 import emcee
-import multiprocessing
 import numpy as np
+import numpy.typing as npt
+import yaml
 
-from bayesian_inference import common_base
-from bayesian_inference import data_IO
-from bayesian_inference import emulation
-from bayesian_inference import log_posterior
+from bayesian_inference import common_base, data_IO, emulation, log_posterior
 
 logger = logging.getLogger(__name__)
 
 
 ####################################################################################################################
-def run_mcmc(config, closure_index=-1):
+def run_mcmc(config: MCMCConfig, closure_index: int =-1) -> None:
     '''
     Run MCMC to compute posterior
 
-    Markov chain Monte Carlo model calibration using the `affine-invariant ensemble
-    sampler (emcee) <http://dfm.io/emcee>`.
-
     :param MCMCConfig config: Instance of MCMCConfig
     :param int closure_index: Index of validation design point to use for MCMC closure. Off by default.
                               If non-negative index is specified, will construct pseudodata from the design point
@@ -46,8 +40,8 @@ def run_mcmc(config, closure_index=-1):
 
     # Get parameter names and min/max
     names = config.analysis_config['parameterization'][config.parameterization]['names']
-    min = config.analysis_config['parameterization'][config.parameterization]['min']
-    max = config.analysis_config['parameterization'][config.parameterization]['max']
+    parameter_min = config.analysis_config['parameterization'][config.parameterization]['min']
+    parameter_max = config.analysis_config['parameterization'][config.parameterization]['max']
     ndim = len(names)
 
     # Load emulators
@@ -66,6 +60,116 @@ def run_mcmc(config, closure_index=-1):
     # In the case of a closure test, we use the pseudodata from the validation design point
     experimental_results = data_IO.data_array_from_h5(config.output_dir, 'observables.h5', pseudodata_index=closure_index, observable_filter=emulation_config.observable_filter)
 
+    if config.mcmc_package == "emcee":
+        _run_using_emcee(
+            config,
+            emulation_config,
+            emulation_results,
+            emulator_cov_unexplained,
+            experimental_results,
+            parameter_min,
+            parameter_max,
+            ndim,
+            closure_index=closure_index,
+        )
+    elif config.mcmc_package == "pocoMC":
+        _run_using_pocoMC(
+            config,
+            emulation_config,
+            emulation_results,
+            emulator_cov_unexplained,
+            experimental_results,
+            parameter_min,
+            parameter_max,
+            ndim,
+            closure_index=closure_index,
+        )
+    else:
+        msg = f"Invalid MCMC sampler: {config.mcmc_package}"
+        raise ValueError(msg)
+
+
+
+####################################################################################################################
+def credible_interval(samples, confidence=0.9, interval_type='quantile'):
+    '''
+    Compute the credible interval for an array of samples.
+
+    TODO: one could also call the versions in pymc3 or arviz
+
+    :param 1darray samples: Array of samples
+    :param float confidence: Confidence level (default 0.9)
+    :param str type: Type of credible interval to compute. Options are:
+                        'hpd' - highest-posterior density
+                        'quantile' - quantile interval
+    '''
+
+    if interval_type == 'hpd':
+        # number of intervals to compute
+        nci = int((1 - confidence)*samples.size)
+        # find highest posterior density (HPD) credible interval i.e. the one with minimum width
+        argp = np.argpartition(samples, [nci, samples.size - nci])
+        cil = np.sort(samples[argp[:nci]])   # interval lows
+        cih = np.sort(samples[argp[-nci:]])  # interval highs
+        ihpd = np.argmin(cih - cil)
+        ci = cil[ihpd], cih[ihpd]
+
+    elif interval_type == 'quantile':
+        cred_range = [(1-confidence)/2, 1-(1-confidence)/2]
+        ci = np.quantile(samples, cred_range)
+
+    return ci
+
+####################################################################################################################
+def map_parameters(posterior, method='quantile'):
+    '''
+    Compute the MAP parameters
+
+    :param 1darray posterior: Array of samples
+    :param str method: Method used to compute MAP. Options are:
+                        'quantile' - take a narrow quantile interval and compute mean of parameters in that interval
+    :return 1darray map_parameters: Array of MAP parameters
+    '''
+
+    if method == 'quantile':
+        central_quantile = 0.01
+        lower_bounds = np.quantile(posterior, 0.5-central_quantile/2, axis=0)
+        upper_bounds = np.quantile(posterior, 0.5+central_quantile/2, axis=0)
+        mask = (posterior >= lower_bounds) & (posterior <= upper_bounds)
+        map_parameters = np.array([posterior[mask[:,i],i].mean() for i in range(posterior.shape[1])])
+
+    return map_parameters
+
+
+def _run_using_emcee(
+    config: MCMCConfig,
+    emulation_config: emulation.EmulationConfig,
+    emulation_results: dict[str, dict[str, npt.NDArray[np.float64]]],
+    emulator_cov_unexplained: dict,
+    experimental_results: dict,
+    parameter_min: npt.NDArray[np.float64],
+    parameter_max: npt.NDArray[np.float64],
+    parameter_ndim: int,
+    closure_index: int,
+) -> None:
+    """Run emcee-based MCMC.
+
+    Markov chain Monte Carlo model calibration using the `affine-invariant ensemble
+    sampler (emcee) <http://dfm.io/emcee>`.
+
+    This is separated out so we can use potentially select other MCMC packages.
+
+    Args:
+        config: MCMC config
+        emulation_config: Emulation configuration
+        emulation_results: Results from the emulator.
+        emulator_cov_unexplained: Covariance of the emulator unexplained variance.
+        experimental_results: Experimental results.
+        parameter_min: Minimum parameter values.
+        parameter_max: Maximum parameter values.
+        parameter_ndim: Number of dimensions of the parameters.
+        closure_index: Index of the closure test design point. If negative, no closure test is performed.
+    """
     # TODO: By default the chain will be stored in memory as a numpy array
     #       If needed we can create a h5py dataset for compression/chunking
 
@@ -75,20 +179,27 @@ def run_mcmc(config, closure_index=-1):
     # NOTE: We use `get_context` here to avoid having to globally specify the context. Plus, it then should be fine
     #       to repeated call this function. (`set_context` can only be called once - otherwise, it's a runtime error).
     ctx = multiprocessing.get_context('spawn')
-    with ctx.Pool(initializer=log_posterior.initialize_pool_variables, initargs=[min, max, emulation_config, emulation_results, experimental_results, emulator_cov_unexplained]) as pool:
+    with ctx.Pool(
+        initializer=log_posterior.initialize_pool_variables,
+        initargs=[
+            parameter_min, parameter_max, emulation_config, emulation_results, experimental_results, emulator_cov_unexplained
+        ]) as pool:
 
         # Construct sampler (we create a dummy daughter class from emcee.EnsembleSampler, to add some logging info)
         # Note: we pass the emulators and experimental data as args to the log_posterior function
         logger.info('Initializing sampler...')
-        sampler = LoggingEnsembleSampler(config.n_walkers, ndim, log_posterior.log_posterior,
-                                        #args=[min, max, emulation_config, emulation_results, experimental_results, emulator_cov_unexplained],
-                                        pool=pool)
+        sampler = LoggingEnsembleSampler(config.n_walkers, parameter_ndim, log_posterior.log_posterior,
+                                         #args=[min, max, emulation_config, emulation_results, experimental_results, emulator_cov_unexplained],
+                                         kwargs={'set_to_infinite_outside_bounds': True},
+                                         pool=pool)
 
         # Generate random starting positions for each walker
-        random_pos = np.random.uniform(min, max, (config.n_walkers, ndim))
+        rng = np.random.default_rng()
+        random_pos = rng.uniform(parameter_min, parameter_max, (config.n_walkers, parameter_ndim))
 
         # Run first half of burn-in
-        logger.info(f'Parallelizing over {pool._processes} processes...')
+        # NOTE-STAT: This code doesn't support not doing burn in
+        logger.info(f'Parallelizing over {pool._processes} processes...')  # type: ignore[attr-defined]
         logger.info('Starting initial burn-in...')
         nburn0 = config.n_burn_steps // 2
         sampler.run_mcmc(random_pos, nburn0, n_logging_steps=config.n_logging_steps)
@@ -116,7 +227,7 @@ def run_mcmc(config, closure_index=-1):
             output_dict['autocorrelation_time'] = sampler.get_autocorr_time()
         except Exception as e:
             output_dict['autocorrelation_time'] = None
-            logger.info(f"Could not compute autocorrelation time: {str(e)}")
+            logger.info(f"Could not compute autocorrelation time: {e!s}")
         # If closure test, save the design point parameters and experimental pseudodata
         if closure_index >= 0:
             design_point =  data_IO.design_array_from_h5(config.output_dir, filename='observables.h5', validation_set=True)[closure_index]
@@ -128,61 +239,11 @@ def run_mcmc(config, closure_index=-1):
         #   e.g. sampler.get_chain(discard=n_burn_steps, thin=thin, flat=True)
         # Note that currently we use sampler.reset() to discard the burn-in and reposition
         #   the walkers (and free memory), but it prevents us from plotting the burn-in samples.
-        with open(config.sampler_outputfile, 'wb') as f:
+        with Path(config.sampler_outputfile).open('wb') as f:
             pickle.dump(sampler, f)
 
         logger.info('Done.')
 
-####################################################################################################################
-def credible_interval(samples, confidence=0.9, interval_type='quantile'):
-    '''
-    Compute the credible interval for an array of samples.
-
-    TODO: one could also call the versions in pymc3 or arviz
-
-    :param 1darray samples: Array of samples
-    :param float confidence: Confidence level (default 0.9)
-    :param str type: Type of credible interval to compute. Options are:
-                        'hpd' - highest-posterior density
-                        'quantile' - quantile interval
-    '''
-
-    if interval_type == 'hpd':
-        # number of intervals to compute
-        nci = int((1 - confidence)*samples.size)
-        # find highest posterior density (HPD) credible interval i.e. the one with minimum width
-        argp = np.argpartition(samples, [nci, samples.size - nci])
-        cil = np.sort(samples[argp[:nci]])   # interval lows
-        cih = np.sort(samples[argp[-nci:]])  # interval highs
-        ihpd = np.argmin(cih - cil)
-        ci = cil[ihpd], cih[ihpd]
-
-    elif interval_type == 'quantile':
-        cred_range = [(1-confidence)/2, 1-(1-confidence)/2]
-        ci = np.quantile(samples, cred_range)
-
-    return ci
-
-####################################################################################################################
-def map_parameters(posterior, method='quantile'):
-    '''
-    Compute the MAP parameters
-
-    :param 1darray posterior: Array of samples
-    :param str method: Method used to compute MAP. Options are:
-                        'quantile' - take a narrow quantile interval and compute mean of parameters in that interval
-    :return 1darray map_parameters: Array of MAP parameters
-    '''
-
-    if method == 'quantile':
-        central_quantile = 0.01
-        lower_bounds = np.quantile(posterior, 0.5-central_quantile/2, axis=0)
-        upper_bounds = np.quantile(posterior, 0.5+central_quantile/2, axis=0)
-        mask = (posterior >= lower_bounds) & (posterior <= upper_bounds)
-        map_parameters = np.array([posterior[mask[:,i],i].mean() for i in range(posterior.shape[1])])
-
-    return map_parameters
-
 ####################################################################################################################
 class LoggingEnsembleSampler(emcee.EnsembleSampler):
     '''
@@ -203,7 +264,174 @@ def run_mcmc(self, X0, n_sampling_steps, n_logging_steps=100, **kwargs):
 
         return result
 
-####################################################################################################################
+
+def _run_using_pocoMC(
+    config: MCMCConfig,
+    emulation_config: emulation.EmulationConfig,
+    emulation_results: dict[str, dict[str, npt.NDArray[np.float64]]],
+    emulator_cov_unexplained: dict,
+    experimental_results: dict,
+    parameter_min: npt.NDArray[np.float64],
+    parameter_max: npt.NDArray[np.float64],
+    parameter_ndim: int,
+    closure_index: int,
+    n_max_steps: int = -1,
+) -> None:
+    """ Run with pocoMC.
+
+    This function is based on PocoMC package (version 1.2.1).
+    pocoMC is a Preconditioned Monte Carlo (PMC) sampler that uses
+    normalizing flows to precondition the target distribution.
+
+    It draws heavily on the wrapper by Hendrick Roch, available at:
+    https://github.com/Hendrik1704/GPBayesTools-HIC/blob/0e41660fafaf1ea2beec3a141a9baa466f31e7c2/src/mcmc.py#L939
+    """
+    # Setup
+    import pocomc as pmc
+    import scipy.stats
+
+    # Validation
+    if n_max_steps < 0:
+        # n_max_steps (int): Maximum number of MCMC steps (default is max_steps=10*n_dim).
+        n_max_steps = 10 * parameter_ndim
+
+    # Additional possible function parameters, but for now, we don't need to pass it in.
+    # random_state (int or None): Initial random seed.
+    random_state = None
+    # pool (int): Number of processes to use for parallelization (default is ``pool=None``).
+    #     If ``pool`` is an integer greater than 1, a ``multiprocessing`` pool is created with the specified number of processes.
+    #pool = None
+
+    # pocoMC config
+    pocoMC_config = PocoMCConfig(
+        analysis_name=config.analysis_name,
+        parameterization=config.parameterization,
+        analysis_config=config.analysis_config,
+        config_file=config.config_file,
+    )
+
+    # Setup the prior distributions
+    logging.info('Generate the prior class for pocoMC ...')
+    prior_distributions = []
+    for p_min, p_max in zip(parameter_min, parameter_max, strict=True):
+        # NOTE: Assuming uniform prior
+        # TODO: Need to update this for c1, c2, and c3, which is uniform in log space.
+        prior_distributions.append(scipy.stats.uniform(p_min, p_max))
+    prior = pmc.Prior(prior_distributions)
+
+    # Create and run the pocoMC sampler
+    # We can use multiprocessing in pocoMC to parallelize the calls to the particles
+    # NOTE: We need to use `spawn` rather than `fork` on linux. Otherwise, the some of the caching mechanisms
+    #       (eg. used in learning the emulator group mapping doesn't work)
+    # NOTE: We use `get_context` here to avoid having to globally specify the context. Plus, it then should be fine
+    #       to repeated call this function. (`set_context` can only be called once - otherwise, it's a runtime error).
+    # NOTE: I create the pool here rather than using the built-in one because I need to initialize the log_posterior!
+    ctx = multiprocessing.get_context('spawn')
+    with ctx.Pool(
+        initializer=log_posterior.initialize_pool_variables,
+        initargs=[
+            parameter_min, parameter_max, emulation_config, emulation_results, experimental_results, emulator_cov_unexplained
+        ]) as pool:
+        logging.info('Starting pocoMC ...')
+        sampler = pmc.Sampler(
+            prior=prior,
+            #likelihood=self.log_likelihood,
+            # TODO: Need initialization function...
+            likelihood=log_posterior.log_posterior,
+            likelihood_kwargs={"set_to_infinite_outside_bounds": False},
+            n_effective=pocoMC_config.n_effective,
+            n_active=pocoMC_config.n_active,
+            n_prior=pocoMC_config.draw_n_prior_samples,
+            sample=pocoMC_config.sampler_type,
+            n_max_steps=n_max_steps,
+            random_state=random_state,
+            vectorize=True,
+            pool=pool
+        )
+        sampler.run(n_total=pocoMC_config.n_total_samples, n_evidence=pocoMC_config.n_importance_samples_for_evidence)
+
+    logging.info('Generate the posterior samples ...')
+    samples, weights, logl, logp = sampler.posterior() # Weighted posterior samples
+
+    logging.info('Generate the evidence ...')
+    logz, logz_err = sampler.evidence() # Bayesian model evidence estimate and uncertainty
+    logger.info(f"Log evidence: {logz}")
+    logger.info(f"Log evidence error: {logz_err}")
+
+    logging.info('Writing pocoMC chains to file...')
+    chain_data = {'chain': samples, 'weights': weights, 'logl': logl,
+                    'logp': logp, 'logz': logz, 'logz_err': logz_err}
+    with config.mcmc_outputfile.open('wb') as file:
+        pickle.dump(chain_data, file)
+
+
+class PocoMCConfig(common_base.CommonBase):
+    """ Configuration class for pocoMC MCMC sampler. """
+    def __init__(self, analysis_name="", parameterization="", analysis_config="", config_file="",
+                       closure_index=-1, **kwargs):
+
+        self.analysis_name = analysis_name
+        self.parameterization = parameterization
+        self.analysis_config = analysis_config
+        self.config_file = Path(config_file)
+
+        with self.config_file.open() as stream:
+            config = yaml.safe_load(stream)
+
+        self.observable_table_dir = config['observable_table_dir']
+        self.observable_config_dir = config['observable_config_dir']
+        self.observables_filename = config["observables_filename"]
+
+        """
+
+        """
+        # NOTE: Do not retrieve this conditionally - if we're asking for it, it's needed.
+        try:
+            mcmc_configuration = analysis_config["parameters"]["mcmc"]["pocoMC"]
+        except KeyError as e:
+            msg = "Please provide pocoMC configuration in the analysis configuration."
+            raise KeyError(msg) from e
+
+        # n_effective (int): The effective sample size maintained during the run (default is n_ess=1000).
+        #self.n_effective = mcmc_configuration.get("n_effective", 1000)
+        # 512 is the default from pocoMC
+        self.n_effective = mcmc_configuration.get("n_effective", 512)
+        # n_active (int): The number of active particles (default is n_active=250). It must be smaller than n_ess.
+        self.n_active = mcmc_configuration.get("n_active", 250)
+        # Validation
+        if self.n_active >= self.n_effective:
+            msg = f"n_active ({self.n_active}) must be smaller than n_effective ({self.n_effective})."
+            raise ValueError(msg)
+
+        # n_prior (int): Number of prior samples to draw (default is n_prior=2*(n_effective//n_active)*n_active).
+        self.draw_n_prior_samples = mcmc_configuration.get("draw_n_prior_samples", 2*(self.n_effective//self.n_active)*self.n_active)
+        # sample (str): Type of MCMC sampler to use (default is sample="pcn").
+        #     Options are ``"pcn"`` (t-preconditioned Crank-Nicolson) or ``"rwm"`` (Random-walk Metropolis).
+        #     t-preconditioned Crank-Nicolson is the default and recommended sampler for PMC as it is more efficient and scales better with the number of parameters.
+        self.sampler_type = mcmc_configuration.get("sampler_type", "tpcn")
+
+        # n_total (int): The total number of effectively independent samples to be collected (default is n_total=5000).
+        # n_evidence (int): The number of importance samples used to estimate the evidence (default is n_evidence=5000).
+        #                     If n_evidence=0, the evidence is not estimated using importance sampling and the SMC estimate is used instead.
+        #                     If preconditioned=False, the evidence is estimated using SMC and n_evidence is ignored.
+        self.n_total_samples = mcmc_configuration.get("n_total_samples", 5000)
+        self.n_importance_samples_for_evidence = mcmc_configuration.get("n_importance_samples_for_evidence", 5000)
+
+        self.output_dir = Path(config['output_dir']) / f'{analysis_name}_{parameterization}'
+        self.emulation_outputfile = Path(self.output_dir) / 'emulation.pkl'
+        self.mcmc_outputfilename = 'mcmc.h5'
+        if closure_index < 0:
+            self.mcmc_output_dir = Path(self.output_dir)
+        else:
+            self.mcmc_output_dir = Path(self.output_dir) / f'closure/results/{closure_index}'
+        self.mcmc_outputfile = Path(self.mcmc_output_dir) / 'mcmc.h5'
+        self.sampler_outputfile = Path(self.mcmc_output_dir) / 'mcmc_sampler.pkl'
+
+        # Update formatting of parameter names for plotting
+        unformatted_names = self.analysis_config['parameterization'][self.parameterization]['names']
+        self.analysis_config['parameterization'][self.parameterization]['names'] = [rf'{s}' for s in unformatted_names]
+
+
 class MCMCConfig(common_base.CommonBase):
 
     #---------------------------------------------------------------
@@ -215,9 +443,9 @@ def __init__(self, analysis_name='', parameterization='', analysis_config='', co
         self.analysis_name = analysis_name
         self.parameterization = parameterization
         self.analysis_config = analysis_config
-        self.config_file = config_file
+        self.config_file = Path(config_file)
 
-        with open(self.config_file, 'r') as stream:
+        with self.config_file.open() as stream:
             config = yaml.safe_load(stream)
 
         self.observable_table_dir = config['observable_table_dir']
@@ -225,20 +453,23 @@ def __init__(self, analysis_name='', parameterization='', analysis_config='', co
         self.observables_filename = config["observables_filename"]
 
         mcmc_configuration = analysis_config["parameters"]["mcmc"]
+        # General arguments
+        self.mcmc_package = mcmc_configuration.get("mcmc_package", "emcee")
+        # emcee specific
         self.n_walkers = mcmc_configuration['n_walkers']
         self.n_burn_steps = mcmc_configuration['n_burn_steps']
         self.n_sampling_steps = mcmc_configuration['n_sampling_steps']
         self.n_logging_steps = mcmc_configuration['n_logging_steps']
 
-        self.output_dir = os.path.join(config['output_dir'], f'{analysis_name}_{parameterization}')
-        self.emulation_outputfile = os.path.join(self.output_dir, 'emulation.pkl')
+        self.output_dir = Path(config['output_dir']) / f'{analysis_name}_{parameterization}'
+        self.emulation_outputfile = Path(self.output_dir) / 'emulation.pkl'
         self.mcmc_outputfilename = 'mcmc.h5'
         if closure_index < 0:
-            self.mcmc_output_dir = self.output_dir
+            self.mcmc_output_dir = Path(self.output_dir)
         else:
-            self.mcmc_output_dir = os.path.join(self.output_dir, f'closure/results/{closure_index}')
-        self.mcmc_outputfile = os.path.join(self.mcmc_output_dir, 'mcmc.h5')
-        self.sampler_outputfile = os.path.join(self.mcmc_output_dir, 'mcmc_sampler.pkl')
+            self.mcmc_output_dir = Path(self.output_dir) / f'closure/results/{closure_index}'
+        self.mcmc_outputfile = Path(self.mcmc_output_dir) / 'mcmc.h5'
+        self.sampler_outputfile = Path(self.mcmc_output_dir) / 'mcmc_sampler.pkl'
 
         # Update formatting of parameter names for plotting
         unformatted_names = self.analysis_config['parameterization'][self.parameterization]['names']
diff --git a/src/bayesian_inference/outliers_smoothing.py b/src/bayesian_inference/outliers_smoothing.py
new file mode 100644
index 0000000..1fd4d05
--- /dev/null
+++ b/src/bayesian_inference/outliers_smoothing.py
@@ -0,0 +1,375 @@
+""" Functionality for identifying outliers and smoothing them.
+
+.. codeauthor:: Raymond Ehlers <raymond.ehlers@cern.ch>, LBL/UCB
+"""
+from __future__ import annotations
+
+import logging
+
+import attrs
+import numpy as np
+import numpy.typing as npt
+import scipy  # type: ignore[import]
+
+logger = logging.getLogger(__name__)
+
+
+IMPLEMENTED_INTERPOLATION_METHODS = ["linear", "cubic_spline"]
+
+@attrs.frozen
+class OutliersConfig:
+    """Configuration for identifying outliers.
+
+    :param float n_RMS: Number of RMS away from the value to identify as an outlier. Default: 2.
+    """
+    n_RMS: float = 2.
+
+
+def find_large_statistical_uncertainty_points(
+    values: npt.NDArray[np.float64],
+    y_err: npt.NDArray[np.float64],
+    outliers_config: OutliersConfig,
+) -> tuple[npt.NDArray[np.int64], npt.NDArray[np.int64]]:
+    """Find problematic points based on large statistical uncertainty points.
+
+    Best to do this observable-by-observable because the relative uncertainty will vary for each one.
+
+    Args:
+        values: The values of the observable, for all design points.
+        y_err: The uncertainties on the values of the observable, for all design points.
+        outliers_config: Configuration for identifying outliers.
+
+    Returns:
+        (n_feature_index, n_design_point_index) of identified outliers
+    """
+    relative_error = y_err / values
+    # This is the rms averaged over all of the design points
+    rms = np.sqrt(np.mean(relative_error**2, axis=-1))
+    # NOTE: Recall that np.where returns (n_feature_index, n_design_point_index) as separate arrays
+    outliers = np.where(relative_error > outliers_config.n_RMS * rms[:, np.newaxis])
+    return outliers  # type: ignore[return-value] # noqa: RET504
+
+
+def find_outliers_based_on_central_values(
+    values: npt.NDArray[np.float64],
+    outliers_config: OutliersConfig,
+) -> tuple[npt.NDArray[np.int64], npt.NDArray[np.int64]]:
+    """Find outlier points based on large deviations from close central values."""
+    # NOTE: We need abs because we don't care about the sign - we just want a measure.
+    diff_between_features = np.abs(np.diff(values, axis=0))
+    rms = np.sqrt(np.mean(diff_between_features**2, axis=-1))
+    outliers_in_diff_mask = (
+        diff_between_features > (outliers_config.n_RMS * rms[:, np.newaxis])
+    )
+    """
+    Now, we need to associate the outliers with the original feature index (ie. taking the diff reduces by one)
+
+    The scheme we'll use to identify problematic points is to take an AND of the left and right of the point.
+    For the first and last index, we cannot take an and since they're one sided. To address this point, we'll
+    redo the exercise, but with the 1th and -2th removed, and take an AND of those and the original. It's ad-hoc,
+    but it gives a second level of cross check for those points.
+    """
+    # First, we'll handle the inner points
+    output = np.zeros_like(values, dtype=np.bool_)
+    output[1:-1, :] = outliers_in_diff_mask[:-1, :] & outliers_in_diff_mask[1:, :]
+
+    # Convenient breakpoint for debugging of high values
+    #if np.any(values > 1.05):
+    #    logger.info(f"{values=}")
+
+    # Now, handle the edges. Here, we need to select the 1th and -2th points
+    if values.shape[0] > 4:
+        s = np.ones(values.shape[0], dtype=np.bool_)
+        s[1] = False
+        s[-2] = False
+        # Now, we'll repeat the calculation with the diff and rMS
+        diff_between_features_for_edges = np.abs(np.diff(values[s, :], axis=0))
+        rms = np.sqrt(np.mean(diff_between_features_for_edges**2, axis=-1))
+        outliers_in_diff_mask_edges = (
+            diff_between_features_for_edges > (outliers_config.n_RMS * rms[:, np.newaxis])
+        )
+        output[0, :] = outliers_in_diff_mask_edges[0, :] & outliers_in_diff_mask[0, :]
+        output[-1, :] = outliers_in_diff_mask_edges[-1, :] & outliers_in_diff_mask[-1, :]
+    else:
+        # Too short - just have to take what we have
+        output[0, :] = outliers_in_diff_mask[0, :]
+        output[-1, :] = outliers_in_diff_mask[-1, :]
+
+    # NOTE: Recall that np.where returns (n_feature_index, n_design_point_index) as separate arrays
+    outliers = np.where(output)
+    return outliers  # type: ignore[return-value] # noqa: RET504
+
+
+def perform_QA_and_reformat_outliers(
+    observable_key: str,
+    outliers: tuple[npt.NDArray[np.int64], npt.NDArray[np.int64]],
+    smoothing_max_n_feature_outliers_to_interpolate: int,
+) -> tuple[dict[int, list[int]], dict[str, dict[int, set[int]]]]:
+    """ Perform QA on identifier outliers, and reformat them for next steps.
+
+    :param observable_key: The key for the observable we're looking at.
+    :param outliers: The outliers provided by the outlier finder.
+    :param smoothing_max_n_feature_outliers_to_interpolate: The maximum number of points to interpolate in a row.
+    """
+    # NOTE: This could skip the observable key, but it's convenient because we then have the same
+    #       format as the overall dict
+    outliers_we_are_unable_to_remove: dict[str, dict[int, set[int]]] = {}
+    # Next, we want to do quality checks.
+    # If there are multiple problematic points in a row, we want to skip interpolation since
+    # it's not clear that we can reliably interpolate.
+    # First, we need to put the features into a more useful order:
+    # outliers: zip(feature_index, design_point) -> dict: (design_point, feature_index)
+    # NOTE: The `design_point` here is the index in the design point array of the design points
+    #       that we've using for this analysis. To actually use them (ie. in print outs), we'll
+    #       need to apply them to the actual design point array.
+    outlier_features_per_design_point: dict[int, set[int]] = {v: set() for v in outliers[1]}
+    for i_feature, design_point in zip(*outliers):
+        outlier_features_per_design_point[design_point].update([i_feature])
+    # These features must be sorted to finding distances between them, but sets are unordered,
+    # so we need to explicitly sort them
+    for design_point in outlier_features_per_design_point:
+        outlier_features_per_design_point[design_point] = sorted(outlier_features_per_design_point[design_point])  # type: ignore[assignment]
+
+    # Since the feature values of one design point shouldn't impact another, we'll want to
+    # check one design point at a time.
+    # NOTE: If we have to skip, we record the design point so we can consider excluding it due
+    #       to that observable.
+    outlier_features_to_interpolate_per_design_point: dict[int, list[int]] = {}
+    #logger.info(f"{observable_key=}, {outlier_features_per_design_point=}")
+    for k, v in outlier_features_per_design_point.items():
+        #logger.debug("------------------------")
+        #logger.debug(f"{k=}, {v=}")
+        # Calculate the distance between the outlier indices
+        distance_between_outliers = np.diff(list(v))
+        # And we'll keep track of which ones pass our quality requirements (not too many in a row).
+        indices_of_outliers_that_are_one_apart = set()
+        accumulated_indices_to_remove = set()
+
+        for distance, lower_feature_index, upper_feature_index in zip(distance_between_outliers, list(v)[:-1], list(v)[1:]):
+            # We're only worried about points which are right next to each other
+            if distance == 1:
+                indices_of_outliers_that_are_one_apart.update([lower_feature_index, upper_feature_index])
+            else:
+                # In this case, we now have points that aren't right next to each other.
+                # Here, we need to figure out what we're going to do with the points that we've found
+                # that **are** right next to each other. Namely, we'll want to remove them from the list
+                # to be interpolated, but if there are more points than our threshold.
+                # NOTE: We want strictly greater than because we add two points per distance being greater than 1.
+                #       eg. one distance(s) of 1 -> two points
+                #           two distance(s) of 1 -> three points (due to set)
+                #           three distance(s) of 1 -> four points (due to set)
+                if len(indices_of_outliers_that_are_one_apart) > smoothing_max_n_feature_outliers_to_interpolate:
+                    # Since we are looking at the distances, we want to remove the points that make up that distance.
+                    accumulated_indices_to_remove.update(indices_of_outliers_that_are_one_apart)
+                else:
+                    # For debugging, keep track of when we find points that are right next to each other but
+                    # where we skip removing them (ie. keep them for interpolation) because they're below our
+                    # max threshold of consecutive points
+                    # NOTE: There's no point in warning if empty, since that case is trivial
+                    if len(indices_of_outliers_that_are_one_apart) > 0:
+                        msg = (
+                            f"Will continue with interpolating consecutive indices {indices_of_outliers_that_are_one_apart}"
+                            f" because the their number is within the allowable range (n_consecutive<={smoothing_max_n_feature_outliers_to_interpolate})."
+                        )
+                        logger.info(msg)
+                # Reset for the next point
+                indices_of_outliers_that_are_one_apart = set()
+        # There are indices left over at the end of the loop which we need to take care of.
+        # eg. If all points are considered outliers
+        if indices_of_outliers_that_are_one_apart and \
+            len(indices_of_outliers_that_are_one_apart) > smoothing_max_n_feature_outliers_to_interpolate:
+            # Since we are looking at the distances, we want to remove the points that make up that distance.
+            #logger.info(f"Ended on {indices_of_outliers_that_are_one_apart=}")
+            accumulated_indices_to_remove.update(indices_of_outliers_that_are_one_apart)
+
+        # Now that we've determine which points we want to remove from our interpolation (accumulated_indices_to_remove),
+        # let's actually remove them from our list.
+        # NOTE: We sort again because sets are not ordered.
+        outlier_features_to_interpolate_per_design_point[k] = sorted(set(v) - accumulated_indices_to_remove)
+        #logger.debug(f"design point {k}: features kept for interpolation: {outlier_features_to_interpolate_per_design_point[k]}")
+
+        # And we'll keep track of what we can't interpolate
+        if accumulated_indices_to_remove:
+            if observable_key not in outliers_we_are_unable_to_remove:
+                outliers_we_are_unable_to_remove[observable_key] = {}
+            outliers_we_are_unable_to_remove[observable_key][k] = accumulated_indices_to_remove
+
+    return outlier_features_to_interpolate_per_design_point, outliers_we_are_unable_to_remove
+
+
+def find_and_smooth_outliers_standalone(
+    observable_key: str,
+    bin_centers: npt.NDArray[np.float64],
+    values: npt.NDArray[np.float64],
+    y_err: npt.NDArray[np.float64],
+    outliers_identification_methods: dict[str, OutliersConfig],
+    smoothing_interpolation_method: str,
+    max_n_points_to_interpolate: int,
+) -> tuple[npt.NDArray[np.float64], npt.NDArray[np.float64], dict[int, set[int]]]:
+    """ A standalone function to identify outliers and smooth them.
+
+    Careful: If you remove design points, you'll need to make sure to keep careful track of the indices!
+
+    Note:
+        For the outliers that we are unable to remove, it's probably best to exclude the design point entirely.
+        However, you'll have to take care of it separately.
+
+    Args:
+        observable_key: The key for the observable we're looking at. Just a name for bookkeeping.
+        bin_centers: The bin centers for the observable.
+        values: The values of the observable, for all design points.
+        y_err: The uncertainties on the values of the observable, for all design points.
+        outliers_identification_methods: The methods to use for identifying outliers. Keys are the methods, while the values
+            are the parameters. Key options: {"large_statistical_errors": OutliersConfig, "large_central_value_difference": OutliersConfig}.
+        smoothing_interpolation_method: The method to use for interpolation. Options: ["linear", "cubic_spline"].
+        max_n_points_to_interpolate: The maximum number of points to interpolate in a row.
+
+    Returns:
+        The smoothed values and uncertainties, and the outliers which we are unable to remove ({feature_index: set(design_point_index)}).
+    """
+    # Validation
+    for outlier_identification_method in outliers_identification_methods:
+        if outlier_identification_method not in ["large_statistical_errors", "large_central_value_difference"]:
+            msg = f"Unrecognized smoothing method {outlier_identification_method}."
+            raise ValueError(msg)
+    if len(bin_centers) == 1:
+        # Skip - we can't interpolate one point.
+        msg = f"Skipping observable \"{observable_key}\" because it has only one point."
+        logger.debug(msg)
+        raise ValueError(msg)
+
+    # Setup
+    outliers_we_are_unable_to_remove: dict[int, set[int]] = {}
+    values = np.array(values, copy=True)
+    y_err = np.array(y_err, copy=True)
+
+    # Identify outliers
+    #outliers = (np.zeros(0, dtype=np.int64), np.zeros(0, dtype=np.int64))
+    outliers = np.zeros((0, 2), dtype=np.int64)
+    for outlier_identification_method, outliers_config in outliers_identification_methods.items():
+        # First, find the outliers based on the selected method
+        if outlier_identification_method == "large_statistical_errors":
+            # large statistical uncertainty points
+            new_outliers = find_large_statistical_uncertainty_points(
+                values=values,
+                y_err=y_err,
+                outliers_config=outliers_config,
+            )
+        elif outlier_identification_method == "large_central_value_difference":
+            # Find additional outliers based on central values which are dramatically different than the others
+            if len(values) > 2:
+                new_outliers = find_outliers_based_on_central_values(
+                    values=values,
+                    outliers_config=outliers_config,
+                )
+            else:
+                new_outliers = ((), ())  # type: ignore[assignment]
+        else:
+            msg = f"Unrecognized outlier identification mode {outlier_identification_method}."
+            raise ValueError(msg)
+        # Merge the outliers together, taking care to deduplicate outlier values that may be stored in each array
+        combined_indices = np.concatenate((outliers, np.column_stack(new_outliers)), axis=0)
+        outliers = np.unique(combined_indices, axis=0)
+
+    # If needed, can split outliers back into the two arrays
+    #outliers_feature_indices, outliers_design_point_indices = outliers[:, 0], outliers[:, 0]
+    outlier_features_to_interpolate_per_design_point, _intermediate_outliers_we_are_unable_to_remove = perform_QA_and_reformat_outliers(
+        observable_key=observable_key,
+        outliers=(outliers[:, 0], outliers[:, 1]),
+        smoothing_max_n_feature_outliers_to_interpolate=max_n_points_to_interpolate,
+    )
+    # And keep track of them
+    outliers_we_are_unable_to_remove.update(_intermediate_outliers_we_are_unable_to_remove.get(observable_key, {}))
+
+    # Perform interpolation
+    for v in [values, y_err]:
+        #logger.info(f"Method: {outlier_identification_method}, Interpolating outliers with {outlier_features_to_interpolate_per_design_point=}, {key_type=}, {observable_key=}, {prediction_key=}")
+        for design_point, points_to_interpolate in outlier_features_to_interpolate_per_design_point.items():
+            try:
+                interpolated_values = perform_interpolation_on_values(
+                    bin_centers=bin_centers,
+                    values_to_interpolate=v[:, design_point],
+                    points_to_interpolate=points_to_interpolate,
+                    smoothing_interpolation_method=smoothing_interpolation_method,
+                )
+                # And assign the interpolated values
+                v[points_to_interpolate, design_point] = interpolated_values
+            except CannotInterpolateDueToOnePointError as e:
+                msg = f"Skipping observable \"{observable_key}\", {design_point=} because {e}"
+                logger.info(msg)
+                # And add to the list since we can't make it work.
+                if design_point not in outliers_we_are_unable_to_remove:
+                    outliers_we_are_unable_to_remove[design_point] = set()
+                outliers_we_are_unable_to_remove[design_point].update(points_to_interpolate)
+                continue
+
+    return values, y_err, outliers_we_are_unable_to_remove
+
+
+
+class CannotInterpolateDueToOnePointError(Exception):
+    """ Error raised when we can't interpolate due to only one point. """
+
+
+def perform_interpolation_on_values(
+    bin_centers: npt.NDArray[np.float64],
+    values_to_interpolate: npt.NDArray[np.float64],
+    points_to_interpolate: list[int],
+    smoothing_interpolation_method: str,
+) -> npt.NDArray[np.float64]:
+    """ Perform interpolation on the requested points to interpolate.
+
+    Args:
+        bin_centers: The bin centers for the observable.
+        values_to_interpolate: The values to interpolate.
+        points_to_interpolate: The points (i.e. bin centers) to interpolate.
+        smoothing_interpolation_method: The method to use for interpolation. Options:
+            ["linear", "cubic_spline"].
+
+    Returns:
+        The values that are interpolated at points_to_interpolate. They cna be inserted into the
+            original values_to_interpolate array via `values_to_interpolate[points_to_interpolate] = interpolated_values`.
+
+    Raises:
+        CannotInterpolateDueToOnePointError: Raised when we can't interpolate due to only
+            one point being left.
+    """
+    # Validation for methods
+    if smoothing_interpolation_method not in IMPLEMENTED_INTERPOLATION_METHODS:
+        msg = f"Unrecognized interpolation method {smoothing_interpolation_method}."
+        raise ValueError(msg)
+
+    # We want to train the interpolation only on all good points, so we take them out.
+    # Otherwise, it will negatively impact the interpolation.
+    mask = np.ones_like(bin_centers, dtype=bool)
+    mask[points_to_interpolate] = False
+
+    # Further validation
+    if len(bin_centers[mask]) == 1:
+        # Skip - we can't interpolate one point.
+        msg = f"Can't interpolate due to only one point left to anchor the interpolation. {mask=}"
+        raise CannotInterpolateDueToOnePointError(msg)
+
+    # NOTE: ROOT::Interpolator uses a Cubic Spline, so this might be a reasonable future approach
+    #       However, I think it's slower, so we'll start with this simple approach.
+    # TODO: We entirely ignore the interpolation error here. Some approaches for trying to account for it:
+    #       - Attempt to combine the interpolation error with the statistical error
+    #       - Randomly remove a few percent of the points which are used for estimating the interpolation,
+    #         and then see if there are significant changes in the interpolated parameters
+    #       - Could vary some parameters (perhaps following the above) and perform the whole
+    #         Bayesian analysis, again looking for how much the determined parameters change.
+    if smoothing_interpolation_method == "linear":
+        interpolated_values = np.interp(
+            bin_centers[points_to_interpolate],
+            bin_centers[mask],
+            values_to_interpolate[mask],
+        )
+    elif smoothing_interpolation_method == "cubic_spline":
+        cs = scipy.interpolate.CubicSpline(
+            bin_centers[mask],
+            values_to_interpolate[mask],
+        )
+        interpolated_values = cs(bin_centers[points_to_interpolate])
+
+    return interpolated_values
+
diff --git a/src/bayesian_inference/plot_analyses.py b/src/bayesian_inference/plot_analyses.py
index a14c601..ca94d54 100644
--- a/src/bayesian_inference/plot_analyses.py
+++ b/src/bayesian_inference/plot_analyses.py
@@ -117,13 +117,13 @@ def plot_qhat_across_analyses(
             suffix = f'E{E}'
             label = f'E = {E} GeV'
             x_array = np.linspace(0.16, 0.5, n_x)
-            qhat_posteriors = np.array([plot_qhat.qhat(posterior_samples, config, T=T, E=E) for T in x_array])
+            qhat_posteriors = np.array([plot_qhat.qhat_over_T_cubed(posterior_samples, config, T=T, E=E) for T in x_array])
         elif T:
             xlabel = 'E (GeV)'
             suffix = f'T{T}'
             label = f'T = {T} GeV'
             x_array = np.linspace(5, 200, n_x)
-            qhat_posteriors = np.array([plot_qhat.qhat(posterior_samples, config, T=T, E=E) for E in x_array])
+            qhat_posteriors = np.array([plot_qhat.qhat_over_T_cubed(posterior_samples, config, T=T, E=E) for E in x_array])
 
         # Plot mean qhat values for each T or E
         qhat_mean = np.mean(qhat_posteriors, axis=1)
@@ -134,9 +134,9 @@ def plot_qhat_across_analyses(
         # Plot the MAP value as well for each T or E
         if plot_map:
             if E:
-                qhat_map = np.array([plot_qhat.qhat(mcmc.map_parameters(posterior_samples), config, T=T, E=E) for T in x_array])
+                qhat_map = np.array([plot_qhat.qhat_over_T_cubed(mcmc.map_parameters(posterior_samples), config, T=T, E=E) for T in x_array])
             elif T:
-                qhat_map = np.array([plot_qhat.qhat(mcmc.map_parameters(posterior_samples), config, T=T, E=E) for E in x_array])
+                qhat_map = np.array([plot_qhat.qhat_over_T_cubed(mcmc.map_parameters(posterior_samples), config, T=T, E=E) for E in x_array])
             ax.plot(x_array, qhat_map, #sns.xkcd_rgb['medium green'],
                     linewidth=2., linestyle='--', label=f'{analysis_label}: MAP')
 
@@ -149,9 +149,9 @@ def plot_qhat_across_analyses(
 
             # Compute qhat for each sample, as a function of T or E
             if E:
-                qhat_priors = np.array([plot_qhat.qhat(prior_samples, config, T=T, E=E) for T in x_array])
+                qhat_priors = np.array([plot_qhat.qhat_over_T_cubed(prior_samples, config, T=T, E=E) for T in x_array])
             elif T:
-                qhat_priors = np.array([plot_qhat.qhat(prior_samples, config, T=T, E=E) for E in x_array])
+                qhat_priors = np.array([plot_qhat.qhat_over_T_cubed(prior_samples, config, T=T, E=E) for E in x_array])
 
             # Get credible interval for each T or E
             h_prior = [mcmc.credible_interval(qhat_values, confidence=cred_level) for qhat_values in qhat_priors]
@@ -174,9 +174,9 @@ def plot_qhat_across_analyses(
         #   boolean array (as a fcn of T or E) of whether the truth value is contained within credible region
         if target_design_point.any():
             if E:
-                qhat_truth = [plot_qhat.qhat(target_design_point, config, T=T, E=E) for T in x_array]
+                qhat_truth = [plot_qhat.qhat_over_T_cubed(target_design_point, config, T=T, E=E) for T in x_array]
             elif T:
-                qhat_truth = [plot_qhat.qhat(target_design_point, config, T=T, E=E) for E in x_array]
+                qhat_truth = [plot_qhat.qhat_over_T_cubed(target_design_point, config, T=T, E=E) for E in x_array]
             ax.plot(x_array, qhat_truth, sns.xkcd_rgb['pale red'],
                     linewidth=2., label='Target')
 
diff --git a/src/bayesian_inference/plot_closure.py b/src/bayesian_inference/plot_closure.py
index d37b0c1..6b51d7b 100644
--- a/src/bayesian_inference/plot_closure.py
+++ b/src/bayesian_inference/plot_closure.py
@@ -110,7 +110,7 @@ def plot(config):
             theta_truth = target_design_point[0][i]
             closure_summary[parameter]['theta_truth'][design_point_index] = theta_truth
             closure_summary[parameter]['theta_closure_array'][design_point_index] = (theta_truth > credible_interval[0]) and (theta_truth < credible_interval[1])
-            closure_summary[parameter]['qhat_mean'][design_point_index] = np.mean(plot_qhat.qhat(target_design_point, config, T=T, E=E))
+            closure_summary[parameter]['qhat_mean'][design_point_index] = np.mean(plot_qhat.qhat_over_T_cubed(target_design_point, config, T=T, E=E))
 
     # Create summary plots over all closure points
     plot_dir = os.path.join(config.output_dir, 'closure/summary_plots')
diff --git a/src/bayesian_inference/plot_input_data.py b/src/bayesian_inference/plot_input_data.py
index 2ee08aa..b2b2229 100644
--- a/src/bayesian_inference/plot_input_data.py
+++ b/src/bayesian_inference/plot_input_data.py
@@ -18,7 +18,7 @@
 import seaborn as sns
 import statsmodels.api as sm
 
-from bayesian_inference import data_IO, emulation, preprocess_input_data
+from bayesian_inference import data_IO, emulation, outliers_smoothing
 
 
 logger = logging.getLogger(__name__)
@@ -203,7 +203,7 @@ def plot(config: emulation.EmulationConfig):
                 config=config,
                 plot_dir=plot_dir,
                 observable_grouping=ObservableGrouping(observable_by_observable=True),
-                outliers_config=preprocess_input_data.OutliersConfig(n_RMS=4.),
+                outliers_config=outliers_smoothing.OutliersConfig(n_RMS=4.),
                 validation_set=validation_set,
                 observables_filename=observables_filename,
             )
@@ -324,7 +324,7 @@ def _plot_pairplot_correlations(
     config: emulation.EmulationConfig,
     plot_dir: Path,
     observable_grouping: ObservableGrouping | None = None,
-    outliers_config: preprocess_input_data.OutliersConfig | None = None,
+    outliers_config: outliers_smoothing.OutliersConfig | None = None,
     annotate_design_points: bool = False,
     use_experimental_data: bool = False,
     validation_set: bool = False,
diff --git a/src/bayesian_inference/plot_qhat.py b/src/bayesian_inference/plot_qhat.py
index e7602c3..d34de84 100644
--- a/src/bayesian_inference/plot_qhat.py
+++ b/src/bayesian_inference/plot_qhat.py
@@ -1,23 +1,21 @@
-#! /usr/bin/env python
 '''
-Module related to generate qhat plots
+Module related to generating qhat plots
 
 authors: J.Mulligan, R.Ehlers
 '''
 
 import logging
-import os
+from pathlib import Path
+from typing import Final
 
+import matplotlib.pyplot as plt
 import numpy as np
-
-from matplotlib import pyplot as plt
+import numpy.typing as npt
 import seaborn as sns
-sns.set_context('paper', rc={'font.size':18,'axes.titlesize':18,'axes.labelsize':18})
 
-from bayesian_inference import data_IO
-from bayesian_inference import emulation
-from bayesian_inference import mcmc
-from bayesian_inference import plot_utils
+from bayesian_inference import data_IO, emulation, mcmc, plot_utils
+
+sns.set_context('paper', rc={'font.size':18,'axes.titlesize':18,'axes.labelsize':18})
 
 logger = logging.getLogger(__name__)
 
@@ -31,7 +29,7 @@ def plot(config):
     '''
 
     # Check if mcmc.h5 file exists
-    if not os.path.exists(config.mcmc_outputfile):
+    if not Path(config.mcmc_outputfile).exists():
         logger.info(f'MCMC output does not exist: {config.mcmc_outputfile}')
         return
 
@@ -41,9 +39,8 @@ def plot(config):
     posterior = results['chain'].reshape((n_walkers*n_steps, n_params))
 
     # Plot output dir
-    plot_dir = os.path.join(config.output_dir, 'plot_qhat')
-    if not os.path.exists(plot_dir):
-        os.makedirs(plot_dir)
+    plot_dir = Path(config.output_dir) / 'plot_qhat'
+    plot_dir.mkdir(parents=True, exist_ok=True)
 
     # qhat plots
     plot_qhat(posterior, plot_dir, config, E=100, cred_level=0.9, n_samples=1000)
@@ -54,7 +51,7 @@ def plot(config):
 
 #---------------------------------------------------------------[]
 def plot_qhat(posterior, plot_dir, config, E=0, T=0, cred_level=0., n_samples=5000, n_x=50,
-              plot_prior=True, plot_mean=True, plot_map=False, target_design_point=np.array([])):
+              plot_prior=True, plot_mean=True, plot_map=False, target_design_point: npt.NDArray[np.int64] | None = None):
     '''
     Plot qhat credible interval from posterior samples,
     as a function of either E or T (with the other held fixed)
@@ -67,12 +64,16 @@ def plot_qhat(posterior, plot_dir, config, E=0, T=0, cred_level=0., n_samples=50
     :param int n_x: number of T or E points to plot
     :param 1darray target_design_point: if closure test, design point corresponding to "truth" qhat value
     '''
+    # Validation
+    if target_design_point is None:
+        target_design_point = np.array([])
 
     # Sample posterior parameters without replacement
     if posterior.shape[0] < n_samples:
         n_samples = posterior.shape[0]
         logger.warning(f'Not enough posterior samples to plot {n_samples} samples, using {n_samples} instead')
-    idx = np.random.choice(posterior.shape[0], size=n_samples, replace=False)
+    rng = np.random.default_rng()
+    idx = rng.choice(posterior.shape[0], size=n_samples, replace=False)
     posterior_samples = posterior[idx,:]
 
     # Compute qhat for each sample (as well as MAP value), as a function of T or E
@@ -82,13 +83,13 @@ def plot_qhat(posterior, plot_dir, config, E=0, T=0, cred_level=0., n_samples=50
         suffix = f'E{E}'
         label = f'E = {E} GeV'
         x_array = np.linspace(0.16, 0.5, n_x)
-        qhat_posteriors = np.array([qhat(posterior_samples, config, T=T, E=E) for T in x_array])
+        qhat_posteriors = np.array([qhat_over_T_cubed(posterior_samples, config, T=T, E=E) for T in x_array])
     elif T:
         xlabel = 'E (GeV)'
         suffix = f'T{T}'
         label = f'T = {T} GeV'
         x_array = np.linspace(5, 200, n_x)
-        qhat_posteriors = np.array([qhat(posterior_samples, config, T=T, E=E) for E in x_array])
+        qhat_posteriors = np.array([qhat_over_T_cubed(posterior_samples, config, T=T, E=E) for E in x_array])
 
     # Plot mean qhat values for each T or E
     if plot_mean:
@@ -99,9 +100,9 @@ def plot_qhat(posterior, plot_dir, config, E=0, T=0, cred_level=0., n_samples=50
     # Plot the MAP value as well for each T or E
     if plot_map:
         if E:
-            qhat_map = np.array([qhat(mcmc.map_parameters(posterior_samples), config, T=T, E=E) for T in x_array])
+            qhat_map = np.array([qhat_over_T_cubed(mcmc.map_parameters(posterior_samples), config, T=T, E=E) for T in x_array])
         elif T:
-            qhat_map = np.array([qhat(mcmc.map_parameters(posterior_samples), config, T=T, E=E) for E in x_array])
+            qhat_map = np.array([qhat_over_T_cubed(mcmc.map_parameters(posterior_samples), config, T=T, E=E) for E in x_array])
         plt.plot(x_array, qhat_map, sns.xkcd_rgb['medium green'],
                 linewidth=2., linestyle='--', label='MAP')
 
@@ -121,9 +122,9 @@ def plot_qhat(posterior, plot_dir, config, E=0, T=0, cred_level=0., n_samples=50
 
         # Compute qhat for each sample, as a function of T or E
         if E:
-            qhat_priors = np.array([qhat(prior_samples, config, T=T, E=E) for T in x_array])
+            qhat_priors = np.array([qhat_over_T_cubed(prior_samples, config, T=T, E=E) for T in x_array])
         elif T:
-            qhat_priors = np.array([qhat(prior_samples, config, T=T, E=E) for E in x_array])
+            qhat_priors = np.array([qhat_over_T_cubed(prior_samples, config, T=T, E=E) for E in x_array])
 
         # Get credible interval for each T or E
         h_prior = [mcmc.credible_interval(qhat_values, confidence=cred_level) for qhat_values in qhat_priors]
@@ -137,9 +138,9 @@ def plot_qhat(posterior, plot_dir, config, E=0, T=0, cred_level=0., n_samples=50
     #   boolean array (as a fcn of T or E) of whether the truth value is contained within credible region
     if target_design_point.any():
         if E:
-            qhat_truth = [qhat(target_design_point, config, T=T, E=E) for T in x_array]
+            qhat_truth = [qhat_over_T_cubed(target_design_point, config, T=T, E=E) for T in x_array]
         elif T:
-            qhat_truth = [qhat(target_design_point, config, T=T, E=E) for E in x_array]
+            qhat_truth = [qhat_over_T_cubed(target_design_point, config, T=T, E=E) for E in x_array]
         plt.plot(x_array, qhat_truth, sns.xkcd_rgb['pale red'],
                 linewidth=2., label='Target')
 
@@ -158,10 +159,12 @@ def plot_qhat(posterior, plot_dir, config, E=0, T=0, cred_level=0., n_samples=50
     elif plot_map:
         ymax = 2*max(qhat_map)
     axes = plt.gca()
-    axes.set_ylim([ymin, ymax])
-    plt.legend(title=f'{label}, {config.parameterization}', title_fontsize=12,
-               loc='upper right', fontsize=12)
+    #axes.set_ylim([ymin, ymax])
+    axes.set_ylim([0, 12])
+    plt.legend(title=f'{label}', title_fontsize=12,
+               loc='upper right', fontsize=12, frameon=False)
 
+    plt.tight_layout()
     plt.savefig(f'{plot_dir}/qhat_{suffix}.pdf')
     plt.close('all')
 
@@ -258,12 +261,42 @@ def _plot_single_parameter_observable_sensitivity(map_parameters, i_parameter, p
                                       linewidth=1, ymin=-5, ymax=5, ylabel=ylabel, plot_exp_data=False, bar_plot=True)
 
 #---------------------------------------------------------------
-def qhat(posterior_samples, config, T=0, E=0) -> float:
+def _running_alpha_s(mu_square: float | npt.NDArray[np.float64], alpha_s: float | npt.NDArray[np.float64]) -> float | npt.NDArray[np.float64]:
+    """ Running alpha_s for HTL-qhat
+
+    Extracted from MATTER:
+    https://github.com/JETSCAPE/JETSCAPE/blob/935b69291f0fd319f42dc6a9fb5960a4f814e16f/src/jet/Matter.cc#L3944-L3953
+
+    We have a separate implementation verified by the theorists:
+    https://github.com/FHead/PhysicsJetScape/blob/c3c9adfeee72e1f9ce34728e174e35ca8a70065b/JetRAAPaper/26363_HPPaperPlots/QHat.h#L10-L19
+
+    Note:
+        lambda_square_QCD_HTL is determined using alpha^fix_s such that the running alpha_s
+        coincide with alpha^fix_s at scale mu^2= 1 GeV^2.
+
+    Args:
+        mu_square: Virtuality of the parton.
+        alpha_s: Coupling constant (here, this is will be alpha^fix_s).
+
+    Returns:
+        float: running alpha_s
+    """
+    if mu_square <= 1.0:
+        return alpha_s
+
+    active_flavor: Final[int] = 3
+    square_lambda_QCD_HTL = np.exp(-12 * np.pi / ((33 - 2 * active_flavor) * alpha_s))
+    return 12 * np.pi / ((33 - 2 * active_flavor) * np.log(mu_square / square_lambda_QCD_HTL))
+
+
+#---------------------------------------------------------------
+def qhat_over_T_cubed(posterior_samples, config, T=0, E=0) -> float:
     '''
     Evaluate qhat/T^3 from posterior samples of parameters,
     for fixed E and T
 
-    See: https://github.com/raymondEhlers/STAT/blob/1b0df83a9fd479f8110fd326ae26c0ce002a1109/run_analysis_base.py
+    See: https://github.com/FHead/PhysicsJetScape/blob/c3c9adfeee72e1f9ce34728e174e35ca8a70065b/JetRAAPaper/26363_HPPaperPlots/QHat.h#L21-L35
+    (which itself is derived from the MATTER code in jetscape).
 
     :param 2darray parameters: posterior samples of parameters -- shape (n_samples, n_params)
     :return 1darray: qhat/T^3 -- shape (n_samples,)
@@ -274,25 +307,33 @@ def qhat(posterior_samples, config, T=0, E=0) -> float:
 
     if config.parameterization == "exponential":
 
+        # Inputs
         alpha_s_fix = posterior_samples[:,0]
-        active_flavor = 3
-        C_a = 3.0  # Extracted from JetScapeConstants
+        # Constants
+        active_flavor: Final[int] = 3
+        # The JETSCAPE framework calculates qhat using the gluon Casimir factor, but
+        # we by convention we typically report the quark qhat value, so we need to use
+        # the quark Casimir factor.
+        C_a: Final[float] = 4.0 / 3.0
 
         # From GeneralQhatFunction
-        debye_mass_square = alpha_s_fix * 4 * np.pi * np.power(T, 2.0) * (6.0 + active_flavor) / 6.0
-        scale_net = 2 * E * T
-        if scale_net < 1.0:
-            scale_net = 1.0
-
-        # alpha_s should be taken as 2*E*T, per Abhijit
-        # See: https://jetscapeworkspace.slack.com/archives/C025X5NE9SN/p1648404101376299
-        square_lambda_QCD_HTL = np.exp( -12.0 * np.pi/( (33 - 2 * active_flavor) * scale_net) )
-        running_alpha_s = 12.0 * np.pi/( (33.0 - 2.0 * active_flavor) * np.log(scale_net/square_lambda_QCD_HTL) )
-        if scale_net < 1.0:
-            running_alpha_s = scale_net
+        debye_mass_square = alpha_s_fix * 4 * np.pi * np.power(T, 2.0) * (6.0 + active_flavor) / 6
+        # This is the virtuality of the parton
+        # See info from Abhijit here: https://jetscapeworkspace.slack.com/archives/C025X5NE9SN/p1648404101376299
+        # as well as Yi's code:
+        # https://github.com/FHead/PhysicsJetScape/blob/c3c9adfeee72e1f9ce34728e174e35ca8a70065b/JetRAAPaper/26363_HPPaperPlots/QHat.h#L21-L35
+        scale_net = np.maximum(2 * E * T, 1.0)
+
+        running_alpha_s = _running_alpha_s(scale_net, alpha_s_fix)
         answer = (C_a * 50.4864 / np.pi) * running_alpha_s * alpha_s_fix * np.abs(np.log(scale_net / debye_mass_square))
 
-        return answer * 0.19732698   # 1/GeV to fm
+        # If we wanted to return just qhat (rather than qhat/T^3), we could use the following conversion:
+        #return answer * 0.19732698   # 1/GeV to fm
+        # qhat/T^3 is dimensionless, so we don't need to convert units
+        return answer  # noqa: RET504
+
+    msg = f"qhat_over_T_cubed not implemented for parameterization: {config.parameterization}"
+    raise RuntimeError(msg)
 
 #---------------------------------------------------------------
 def _generate_prior_samples(config, n_samples=100):
@@ -316,11 +357,12 @@ def _generate_prior_samples(config, n_samples=100):
             parameter_max[i] = np.log(parameter_max[i])
 
     # Generate uniform samples
-    samples = np.random.uniform(parameter_min, parameter_max, (n_samples, n_params))
+    rng = np.random.default_rng()
+    samples = rng.uniform(parameter_min, parameter_max, (n_samples, n_params))
 
     # Transform log(c1,c2,c3) back to c1,c2,c3
     for i,name in enumerate(names):
         if 'c_' in name:
             samples[:,i] = np.exp(samples[:,i])
 
-    return samples
\ No newline at end of file
+    return samples
diff --git a/src/bayesian_inference/plot_utils.py b/src/bayesian_inference/plot_utils.py
index c32c1bd..865b319 100644
--- a/src/bayesian_inference/plot_utils.py
+++ b/src/bayesian_inference/plot_utils.py
@@ -1,4 +1,3 @@
-#! /usr/bin/env python
 '''
 Module with plotting utilities that can be shared across multiple other plotting modules
 
diff --git a/src/bayesian_inference/preprocess_input_data.py b/src/bayesian_inference/preprocess_input_data.py
index 5c30db1..50e5973 100644
--- a/src/bayesian_inference/preprocess_input_data.py
+++ b/src/bayesian_inference/preprocess_input_data.py
@@ -12,22 +12,12 @@
 import attrs
 import numpy as np
 import numpy.typing as npt
-import scipy.interpolate
 import yaml
 
-from bayesian_inference import common_base, data_IO
+from bayesian_inference import common_base, data_IO, outliers_smoothing
 
 logger = logging.getLogger(__name__)
 
-@attrs.frozen
-class OutliersConfig:
-    """Configuration for identifying outliers.
-
-    :param float n_RMS: Number of RMS away from the value to identify as an outlier. Default: 2.
-    """
-    n_RMS: float = 2.
-
-
 def preprocess(
     preprocessing_config: PreprocessingConfig,
 ) -> dict[str, Any]:
@@ -43,6 +33,7 @@ def preprocess(
 
     return observables
 
+
 def steer_find_physics_motivated_outliers(
     observables: dict[str, dict[str, dict[str, Any]]],
     preprocessing_config: PreprocessingConfig,
@@ -54,6 +45,7 @@ def steer_find_physics_motivated_outliers(
             validation_set=validation_set,
         )
 
+
 def _find_physics_motivated_outliers(
     observables: dict[str, dict[str, dict[str, Any]]],
     preprocessing_config: PreprocessingConfig,
@@ -188,7 +180,7 @@ def _smooth_statistical_outliers_in_predictions(
         # First, find the outliers based on the selected method
         if outlier_identification_method == "large_statistical_errors":
             # large statistical uncertainty points
-            outliers = _find_large_statistical_uncertainty_points(
+            outliers = outliers_smoothing.find_large_statistical_uncertainty_points(
                 values=all_observables[prediction_key][observable_key]["y"],
                 y_err=all_observables[prediction_key][observable_key]["y_err"],
                 outliers_config=preprocessing_config.smoothing_outliers_config,
@@ -196,7 +188,7 @@ def _smooth_statistical_outliers_in_predictions(
         elif outlier_identification_method == "large_central_value_difference":
             # Find additional outliers based on central values which are dramatically different than the others
             if len(all_observables[prediction_key][observable_key]["y"]) > 2:
-                outliers = _find_outliers_based_on_central_values(
+                outliers = outliers_smoothing.find_outliers_based_on_central_values(
                     values=all_observables[prediction_key][observable_key]["y"],
                     outliers_config=preprocessing_config.smoothing_outliers_config,
                 )
@@ -213,10 +205,10 @@ def _smooth_statistical_outliers_in_predictions(
         #]
 
         # Perform quality assurance and reformat outliers
-        outlier_features_to_interpolate_per_design_point, _intermediate_outliers_we_are_unable_to_remove = _perform_QA_and_reformat_outliers(
+        outlier_features_to_interpolate_per_design_point, _intermediate_outliers_we_are_unable_to_remove = outliers_smoothing.perform_QA_and_reformat_outliers(
             observable_key=observable_key,
             outliers=outliers,
-            preprocessing_config=preprocessing_config,
+            smoothing_max_n_feature_outliers_to_interpolate=preprocessing_config.smoothing_max_n_feature_outliers_to_interpolate,
         )
         # Only fill if we actually have something to report
         if observable_key in _intermediate_outliers_we_are_unable_to_remove:
@@ -243,15 +235,16 @@ def _smooth_statistical_outliers_in_predictions(
 
             #logger.info(f"Method: {outlier_identification_method}, Interpolating outliers with {outlier_features_to_interpolate_per_design_point=}, {key_type=}, {observable_key=}, {prediction_key=}")
             for design_point, points_to_interpolate in outlier_features_to_interpolate_per_design_point.items():
-                # We want to train the interpolation only on all good points, so we make them out.
-                # Otherwise, it will negatively impact the interpolation.
-                mask = np.ones_like(observable_bin_centers, dtype=bool)
-                mask[points_to_interpolate] = False
-
-                # Validation
-                if len(observable_bin_centers[mask]) == 1:
-                    # Skip - we can't interpolate one point.
-                    msg = f"Skipping observable \"{observable_key}\", {design_point=} because it has only one point to anchor the interpolation. {mask=}"
+                try:
+                    interpolated_values = outliers_smoothing.perform_interpolation_on_values(
+                        bin_centers=observable_bin_centers,
+                        values_to_interpolate=new_observables[prediction_key][observable_key][key_type][:, design_point],
+                        points_to_interpolate=points_to_interpolate,
+                        smoothing_interpolation_method=preprocessing_config.smoothing_interpolation_method,
+                    )
+                    new_observables[prediction_key][observable_key][key_type][points_to_interpolate, design_point] = interpolated_values
+                except outliers_smoothing.CannotInterpolateDueToOnePointError as e:
+                    msg = f"Skipping observable \"{observable_key}\", {design_point=} because {e}"
                     logger.info(msg)
                     # And add to the list since we can't make it work.
                     if observable_key not in outliers_we_are_unable_to_remove:
@@ -261,29 +254,6 @@ def _smooth_statistical_outliers_in_predictions(
                     outliers_we_are_unable_to_remove[observable_key][design_point].update(points_to_interpolate)
                     continue
 
-                # NOTE: ROOT::Interpolator uses a Cubic Spline, so this might be a reasonable future approach
-                #       However, I think it's slower, so we'll start with this simple approach.
-                # TODO: We entirely ignore the interpolation error here. Some approaches for trying to account for it:
-                #       - Attempt to combine the interpolation error with the statistical error
-                #       - Randomly remove a few percent of the points which are used for estimating the interpolation,
-                #         and then see if there are significant changes in the interpolated parameters
-                #       - Could vary some parameters (perhaps following the above) and perform the whole
-                #         Bayesian analysis, again looking for how much the determined parameters change.
-                if preprocessing_config.smoothing_interpolation_method == "linear":
-                    interpolated_values = np.interp(
-                        observable_bin_centers[points_to_interpolate],
-                        observable_bin_centers[mask],
-                        new_observables[prediction_key][observable_key][key_type][:, design_point][mask],
-                    )
-                elif preprocessing_config.smoothing_interpolation_method == "cubic_spline":
-                    cs = scipy.interpolate.CubicSpline(
-                        observable_bin_centers[mask],
-                        new_observables[prediction_key][observable_key][key_type][:, design_point][mask],
-                    )
-                    interpolated_values = cs(observable_bin_centers[points_to_interpolate])
-
-                new_observables[prediction_key][observable_key][key_type][points_to_interpolate, design_point] = interpolated_values
-
     # Reformat the outliers_we_are_unable_to_remove to be more useful and readable
     #logger.info(
     #    f"Observables which we are unable to remove outliers from: {outliers_we_are_unable_to_remove}"
@@ -291,7 +261,7 @@ def _smooth_statistical_outliers_in_predictions(
     # NOTE: The typing is wrong because I based the type annotations on the "Predictions" key only,
     #       since it's more useful here.
     # NOTE: We need to map the i_design_point to the actual design point indices for them to be useful!
-    design_point_array: npt.NDArray[np.intp] = all_observables["Design_indices" + ("_validation" if validation_set else "")]  # type: ignore[assignment]
+    design_point_array: npt.NDArray[np.int64] = all_observables["Design_indices" + ("_validation" if validation_set else "")]  # type: ignore[assignment]
     design_points_we_may_want_to_remove: dict[int, dict[str, set[int]]] = {}
     for observable_key, _v in outliers_we_are_unable_to_remove.items():
         for i_design_point, i_feature in _v.items():
@@ -310,169 +280,6 @@ def _smooth_statistical_outliers_in_predictions(
 
     return new_observables
 
-def _perform_QA_and_reformat_outliers(
-    observable_key: str,
-    outliers: tuple[npt.NDArray[np.intp], npt.NDArray[np.intp]],
-    preprocessing_config: PreprocessingConfig,
-) -> tuple[dict[int, list[int]], dict[str, dict[int, set[int]]]]:
-    """ Perform QA on identifier outliers, and reformat them for next steps.
-
-    :param observable_key: The key for the observable we're looking at.
-    :param outliers: The outliers provided by the outlier finder.
-    :param preprocessing_config: Configuration for preprocessing.
-    """
-    # NOTE: This could skip the observable key, but it's convenient because we then have the same
-    #       format as the overall dict
-    outliers_we_are_unable_to_remove: dict[str, dict[int, set[int]]] = {}
-    # Next, we want to do quality checks.
-    # If there are multiple problematic points in a row, we want to skip interpolation since
-    # it's not clear that we can reliably interpolate.
-    # First, we need to put the features into a more useful order:
-    # outliers: zip(feature_index, design_point) -> dict: (design_point, feature_index)
-    # NOTE: The `design_point` here is the index in the design point array of the design points
-    #       that we've using for this analysis. To actually use them (ie. in print outs), we'll
-    #       need to apply them to the actual design point array.
-    outlier_features_per_design_point: dict[int, set[int]] = {v: set() for v in outliers[1]}
-    for i_feature, design_point in zip(*outliers):
-        outlier_features_per_design_point[design_point].update([i_feature])
-    # These features must be sorted to finding distances between them, but sets are unordered,
-    # so we need to explicitly sort them
-    for design_point in outlier_features_per_design_point:
-        outlier_features_per_design_point[design_point] = sorted(outlier_features_per_design_point[design_point])  # type: ignore[assignment]
-
-    # Since the feature values of one design point shouldn't impact another, we'll want to
-    # check one design point at a time.
-    # NOTE: If we have to skip, we record the design point so we can consider excluding it due
-    #       to that observable.
-    outlier_features_to_interpolate_per_design_point: dict[int, list[int]] = {}
-    #logger.info(f"{observable_key=}, {outlier_features_per_design_point=}")
-    for k, v in outlier_features_per_design_point.items():
-        #logger.debug("------------------------")
-        #logger.debug(f"{k=}, {v=}")
-        # Calculate the distance between the outlier indices
-        distance_between_outliers = np.diff(list(v))
-        # And we'll keep track of which ones pass our quality requirements (not too many in a row).
-        indices_of_outliers_that_are_one_apart = set()
-        accumulated_indices_to_remove = set()
-
-        for distance, lower_feature_index, upper_feature_index in zip(distance_between_outliers, list(v)[:-1], list(v)[1:]):
-            # We're only worried about points which are right next to each other
-            if distance == 1:
-                indices_of_outliers_that_are_one_apart.update([lower_feature_index, upper_feature_index])
-            else:
-                # In this case, we now have points that aren't right next to each other.
-                # Here, we need to figure out what we're going to do with the points that we've found
-                # that **are** right next to each other. Namely, we'll want to remove them from the list
-                # to be interpolated, but if there are more points than our threshold.
-                # NOTE: We want strictly greater than because we add two points per distance being greater than 1.
-                #       eg. one distance(s) of 1 -> two points
-                #           two distance(s) of 1 -> three points (due to set)
-                #           three distance(s) of 1 -> four points (due to set)
-                if len(indices_of_outliers_that_are_one_apart) > preprocessing_config.smoothing_max_n_feature_outliers_to_interpolate:
-                    # Since we are looking at the distances, we want to remove the points that make up that distance.
-                    accumulated_indices_to_remove.update(indices_of_outliers_that_are_one_apart)
-                else:
-                    # For debugging, keep track of when we find points that are right next to each other but
-                    # where we skip removing them (ie. keep them for interpolation) because they're below our
-                    # max threshold of consecutive points
-                    # NOTE: There's no point in warning if empty, since that case is trivial
-                    if len(indices_of_outliers_that_are_one_apart) > 0:
-                        msg = (
-                            f"Will continue with interpolating consecutive indices {indices_of_outliers_that_are_one_apart}"
-                            f" because the their number is within the allowable range (n_consecutive<={preprocessing_config.smoothing_max_n_feature_outliers_to_interpolate})."
-                        )
-                        logger.info(msg)
-                # Reset for the next point
-                indices_of_outliers_that_are_one_apart = set()
-        # There are indices left over at the end of the loop which we need to take care of.
-        # eg. If all points are considered outliers
-        if indices_of_outliers_that_are_one_apart:
-            if len(indices_of_outliers_that_are_one_apart) > preprocessing_config.smoothing_max_n_feature_outliers_to_interpolate:
-                # Since we are looking at the distances, we want to remove the points that make up that distance.
-                #logger.info(f"Ended on {indices_of_outliers_that_are_one_apart=}")
-                accumulated_indices_to_remove.update(indices_of_outliers_that_are_one_apart)
-
-        # Now that we've determine which points we want to remove from our interpolation (accumulated_indices_to_remove),
-        # let's actually remove them from our list.
-        # NOTE: We sort again because sets are not ordered.
-        outlier_features_to_interpolate_per_design_point[k] = sorted(list(set(v) - accumulated_indices_to_remove))
-        #logger.debug(f"design point {k}: features kept for interpolation: {outlier_features_to_interpolate_per_design_point[k]}")
-
-        # And we'll keep track of what we can't interpolate
-        if accumulated_indices_to_remove:
-            if observable_key not in outliers_we_are_unable_to_remove:
-                outliers_we_are_unable_to_remove[observable_key] = {}
-            outliers_we_are_unable_to_remove[observable_key][k] = accumulated_indices_to_remove
-
-    return outlier_features_to_interpolate_per_design_point, outliers_we_are_unable_to_remove
-
-
-def _find_large_statistical_uncertainty_points(
-    values: npt.NDArray[np.float64],
-    y_err: npt.NDArray[np.float64],
-    outliers_config: OutliersConfig,
-) -> tuple[npt.NDArray[np.intp], npt.NDArray[np.intp]]:
-    """Find problematic points based on large statistical uncertainty points.
-
-    Best to do this observable-by-observable because the relative uncertainty will vary for each one.
-    """
-    relative_error = y_err / values
-    # This is the rms averaged over all of the design points
-    rms = np.sqrt(np.mean(relative_error**2, axis=-1))
-    # NOTE: Recall that np.where returns (n_feature_index, n_design_point_index) as separate arrays
-    outliers = np.where(relative_error > outliers_config.n_RMS * rms[:, np.newaxis])
-    return outliers  # type: ignore[return-value]
-
-
-def _find_outliers_based_on_central_values(
-    values: npt.NDArray[np.float64],
-    outliers_config: OutliersConfig,
-) -> tuple[npt.NDArray[np.intp], npt.NDArray[np.intp]]:
-    """Find outlier points based on large deviations from close central values."""
-    # NOTE: We need abs because we don't care about the sign - we just want a measure.
-    diff_between_features = np.abs(np.diff(values, axis=0))
-    rms = np.sqrt(np.mean(diff_between_features**2, axis=-1))
-    outliers_in_diff_mask = (
-        diff_between_features > (outliers_config.n_RMS * rms[:, np.newaxis])
-    )
-    """
-    Now, we need to associate the outliers with the original feature index (ie. taking the diff reduces by one)
-
-    The scheme we'll use to identify problematic points is to take an AND of the left and right of the point.
-    For the first and last index, we cannot take an and since they're one sided. To address this point, we'll
-    redo the exercise, but with the 1th and -2th removed, and take an AND of those and the original. It's ad-hoc,
-    but it gives a second level of cross check for those points.
-    """
-    # First, we'll handle the inner points
-    output = np.zeros_like(values, dtype=np.bool_)
-    output[1:-1, :] = outliers_in_diff_mask[:-1, :] & outliers_in_diff_mask[1:, :]
-
-    # Convenient breakpoint for debugging of high values
-    #if np.any(values > 1.05):
-    #    logger.info(f"{values=}")
-
-    # Now, handle the edges. Here, we need to select the 1th and -2th points
-    if values.shape[0] > 4:
-        s = np.ones(values.shape[0], dtype=np.bool_)
-        s[1] = False
-        s[-2] = False
-        # Now, we'll repeat the calculation with the diff and rMS
-        diff_between_features_for_edges = np.abs(np.diff(values[s, :], axis=0))
-        rms = np.sqrt(np.mean(diff_between_features_for_edges**2, axis=-1))
-        outliers_in_diff_mask_edges = (
-            diff_between_features_for_edges > (outliers_config.n_RMS * rms[:, np.newaxis])
-        )
-        output[0, :] = outliers_in_diff_mask_edges[0, :] & outliers_in_diff_mask[0, :]
-        output[-1, :] = outliers_in_diff_mask_edges[-1, :] & outliers_in_diff_mask[-1, :]
-    else:
-        # Too short - just have to take what we have
-        output[0, :] = outliers_in_diff_mask[0, :]
-        output[-1, :] = outliers_in_diff_mask[-1, :]
-
-    # NOTE: Recall that np.where returns (n_feature_index, n_design_point_index) as separate arrays
-    outliers = np.where(output)
-    return outliers  # type: ignore[return-value]
-
 
 @attrs.define
 class PreprocessingConfig(common_base.CommonBase):
@@ -490,10 +297,10 @@ def __attrs_post_init__(self):
         # Retrieve parameters from the config
         # Smoothing parameters
         smoothing_parameters = self.analysis_config['parameters']['preprocessing']['smoothing']
-        self.smoothing_outliers_config = OutliersConfig(n_RMS=smoothing_parameters["outlier_n_RMS"])
+        self.smoothing_outliers_config = outliers_smoothing.OutliersConfig(n_RMS=smoothing_parameters["outlier_n_RMS"])
         self.smoothing_interpolation_method = smoothing_parameters["interpolation_method"]
         # Validation
-        if self.smoothing_interpolation_method not in ["linear", "cubic_spline"]:
+        if self.smoothing_interpolation_method not in outliers_smoothing.IMPLEMENTED_INTERPOLATION_METHODS:
             msg = f"Unrecognized interpolation method {self.smoothing_interpolation_method}."
             raise ValueError(msg)
         self.smoothing_max_n_feature_outliers_to_interpolate = smoothing_parameters["max_n_feature_outliers_to_interpolate"]
diff --git a/tests/test_outliers_smoothing.py b/tests/test_outliers_smoothing.py
new file mode 100644
index 0000000..6149e14
--- /dev/null
+++ b/tests/test_outliers_smoothing.py
@@ -0,0 +1,47 @@
+"""Tests for standalone smoothing functions.
+
+"""
+
+from __future__ import annotations
+
+import logging
+from pathlib import Path
+
+import numpy as np
+import pytest  # noqa: F401
+
+from bayesian_inference import outliers_smoothing
+
+logger = logging.getLogger(__name__)
+
+_data_dir = Path(__file__).parent / "test_data"
+
+
+def test_smoothing() -> None:
+    # Setup: Load data
+    measured_data = np.loadtxt(_data_dir / "tables" / "Data" / "Data__5020__PbPb__hadron__pt_ch_cms____0-5.dat", ndmin=2)
+    # Calculate bin centers from data
+    x_min = measured_data[:, 0]
+    x_max = measured_data[:, 1]
+    bin_centers = x_min + (x_max - x_min) / 2.
+    # And load values and errors
+    values = np.loadtxt(_data_dir / "tables" / "Prediction" / "Prediction__exponential__5020__PbPb__hadron__pt_ch_cms____0-5__values.dat", ndmin=2)
+    y_err = np.loadtxt(_data_dir / "tables" / "Prediction" / "Prediction__exponential__5020__PbPb__hadron__pt_ch_cms____0-5__errors.dat", ndmin=2)
+
+    # Identify outliers and smooth them
+    output_values, output_y_err, outliers_that_cannot_be_removed = outliers_smoothing.find_and_smooth_outliers_standalone(
+        observable_key="hadron__pt_ch_cms",
+        bin_centers=bin_centers,
+        values=values,
+        y_err=y_err,
+        # Default values as of September 2024
+        outliers_identification_methods={
+            "large_statistical_errors": outliers_smoothing.OutliersConfig(n_RMS=2),
+            "large_central_value_difference": outliers_smoothing.OutliersConfig(n_RMS=2),
+        },
+        smoothing_interpolation_method="linear",
+        max_n_points_to_interpolate=2,
+    )
+
+    assert not np.allclose(output_values, values)
+    assert not np.allclose(output_y_err, y_err)