diff --git a/.gitignore b/.gitignore
index 8ef9160b..43d0f951 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,7 +1,6 @@
-scratch_*
-*ipynb_checkpoints
-*.DS_Store
-*__pycache__
-build/*
-epsie.egg-info/*
+build/
+epsie.egg-info/
+.DS_Store
 reinstall_epsie.sh
+*.pyc
+scratch_*
diff --git a/epsie/diagnostic/__init__.py b/epsie/diagnostic/__init__.py
new file mode 100644
index 00000000..e940070d
--- /dev/null
+++ b/epsie/diagnostic/__init__.py
@@ -0,0 +1,17 @@
+# Copyright (C) 2019  Collin Capano
+# This program is free software; you can redistribute it and/or modify it
+# under the terms of the GNU General Public License as published by the
+# Free Software Foundation; either version 3 of the License, or (at your
+# option) any later version.
+#
+# This program is distributed in the hope that it will be useful, but
+# WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General
+# Public License for more details.
+#
+# You should have received a copy of the GNU General Public License along
+# with this program; if not, write to the Free Software Foundation, Inc.,
+# 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+
+from .acl import acl_1d, acl_chain, thinned_samples
+from .convergence import gelman_rubin_test
diff --git a/epsie/diagnostic/acl.py b/epsie/diagnostic/acl.py
new file mode 100644
index 00000000..6aae3a24
--- /dev/null
+++ b/epsie/diagnostic/acl.py
@@ -0,0 +1,222 @@
+# Copyright (C) 2022 Richard Stiskalek, Collin Capano
+# This program is free software; you can redistribute it and/or modify it
+# under the terms of the GNU General Public License as published by the
+# Free Software Foundation; either version 3 of the License, or (at your
+# option) any later version.
+#
+# This program is distributed in the hope that it will be useful, but
+# WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General
+# Public License for more details.
+#
+# You should have received a copy of the GNU General Public License along
+# with this program; if not, write to the Free Software Foundation, Inc.,
+# 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+
+"""Autocorrelation time calculation."""
+import numpy
+
+from epsie.samplers import MetropolisHastingsSampler, ParallelTemperedSampler
+
+
+def acl_1d(x, c=5.0):
+    """
+    Calculate the autocorrelation length (ACL) of some series.
+
+    Algorithm used is from:
+    N. Madras and A.D. Sokal, J. Stat. Phys. 50, 109 (1988).
+
+    Implementation from:
+    https://emcee.readthedocs.io/en/stable/tutorials/autocorr/#autocorr
+
+    Arguments
+    ---------
+    x : 1-dimensional array
+        Samples whose autocorrelation length is to be calculated.
+    c : float, optional
+        ACL hyperparameter. As per Sokal by default set to 5.
+
+    Returns
+    -------
+    ACL: int
+        Autocorrelation length.
+    """
+    if x.ndim != 1:
+        raise TypeError("``x`` not a 1D array. Currently {}".format(x.ndim))
+    # n is the next power of 2 for length of x
+    n = (2**numpy.ceil(numpy.log2(x.size))).astype(int)
+    # Compute the FFT and then (from that) the auto-correlation function
+    f = numpy.fft.fft(x - numpy.mean(x), n=2 * n)
+    acf = numpy.fft.ifft(f * numpy.conjugate(f))[: len(x)].real / (4 * n)
+
+    acf /= acf[0]
+
+    taus = 2.0 * numpy.cumsum(acf) - 1.0
+    window = auto_window(taus, c)
+    acl = numpy.ceil(taus[window]).astype(int)
+    if acl < 1:
+        acl = 1
+    return acl
+
+
+def auto_window(taus, c):
+    """
+    ACL automated windowing procedure following Sokal (1989).
+
+    Implementation from:
+    https://emcee.readthedocs.io/en/stable/tutorials/autocorr/#autocorr
+    """
+    m = numpy.arange(len(taus)) < c * taus
+    if numpy.any(m):
+        return numpy.argmin(m)
+    return len(taus) - 1
+
+
+def acl_chain(chain, burnin_iter=0, c=5.0, full=False):
+    """
+    Calculate the ACL of :py:class:`epsie.chain.Chain` chain.
+
+    Arguments
+    ---------
+    chain : :py:class:`epsie.chain.Chain`
+        Epsie chain.
+    burnin_iter : int, optional
+        Number of burnin iterations to be thrown away.
+    c : float, optional
+        ACL calculation hyperparameter. By default 5.
+    full : bool, optionall
+        Whether to return the ACL of every parameter. By default False, thus
+        returning only the maximum ACL.
+
+    Returns
+    -------
+    ACL : int or array of integers
+        Chain's ACL(s).
+    """
+    acls = [acl_1d(chain.positions[p][burnin_iter:]) for p in chain.parameters]
+    if full:
+        return acls
+    return max(acls)
+
+
+def thinned_samples(sampler, burnin_iter=0, c=5.0, temp_acls_method="coldest"):
+    """
+    Parse a sampler and return its samples thinned by the ACL.
+
+    Arguments
+    ---------
+    sampler : {:py:class:`epsie.sampler.MetropolisHastingsSampler`,
+               :py:class:`epsie.sampler.ParallelTemperedSampler`}
+        Epsie sampler whose samples to extract.
+    burnin_iter : int, optional
+        Number of burnin iterations to be thrown away.
+    c : float, optional
+        ACL calculation hyperparameter. By default 5.
+    temp_acls_method : string, optional
+        Tempered acls selection, either `coldest` or `max`. The former
+        corresponds to taking the ACL of the coldest chain, while the latter to
+        the maximum ACL across all temperatures. This single ACL is then used
+        to thin all temperatures.
+
+    Returns
+    -------
+    thinned samples : structured array
+        Array whose `dtype.names` are the sampler parameters. Each parameter's
+        data is 1-dimensional for the MH sampler and 2-dimensional for the PT
+        sampler. In the latter case the first and second axis represent the
+        temperature and sample index.
+    """
+    if isinstance(sampler, MetropolisHastingsSampler):
+        return _thinned_mh_samples(sampler, burnin_iter, c)
+    elif isinstance(sampler, ParallelTemperedSampler):
+        return _thinned_pt_samples(sampler, burnin_iter, c, temp_acls_method)
+    else:
+        raise ValueError("Unknown sampler type ``{}``".format(type(sampler)))
+
+
+def _get_raw_data(sampler, burnin_iter):
+    raw = {}
+    raw.update({p: sampler.positions[..., burnin_iter:][p]
+                for p in sampler.parameters})
+    raw.update({p: sampler.stats[..., burnin_iter:][p]
+                for p in ("logl", "logp")})
+    if sampler.blobs is not None:
+        raw.update({p: sampler.blobs[..., burnin_iter:][p]
+                    for p in sampler.blobs.dtype.names})
+    return raw
+
+
+def _thinned_mh_samples(sampler, burnin_iter=0, c=5.0):
+    # Calculate the ACL for each chain
+    acls = [acl_chain(chain, burnin_iter, c) for chain in sampler.chains]
+
+    keys = sampler.parameters + ("logl", "logp")
+    keys += sampler.blobs.dtype.names if sampler.blobs is not None else ()
+    raw = _get_raw_data(sampler, burnin_iter)
+
+    # Cycle over the chains and thin them
+    _thinned = {p: [] for p in keys}
+    for ii in range(sampler.nchains):
+        for key in keys:
+            _thinned[key].append(raw[key][ii, :][::-1][::acls[ii]][::-1])
+
+    # Put the thinned samples into a structured array
+    dtype = sampler.positions.dtype.descr + sampler.stats.dtype.descr
+    if sampler.blobs is not None:
+        dtype += sampler.blobs.dtype.descr
+    thinned = numpy.zeros(sum(x.size for x in _thinned[keys[0]]),
+                          dtype=numpy.dtype(dtype))
+    for p in keys:
+        thinned[p] = numpy.concatenate(_thinned[p])
+
+    return thinned
+
+
+def _thinned_pt_samples(sampler, burnin_iter=0, c=5.0,
+                        temp_acls_method="coldest"):
+    allowed_methods = ["coldest", "max"]
+    if temp_acls_method not in allowed_methods:
+        raise ValueError("`Invalid `temp_acls_method`. Allowed methods: `{}`"
+                         .format(allowed_methods))
+    # Calculate the ACL across temperatures for each chain
+    temp_acls = numpy.zeros((sampler.nchains, sampler.ntemps), dtype=int)
+    for ii in range(sampler.nchains):
+        for jj in range(sampler.ntemps):
+            temp_acls[ii, jj] = acl_chain(
+                sampler.chains[ii].chains[jj], burnin_iter, c=c)
+            # By default we only take the coldest chain. No need to calculate
+            # the hotter chains then.
+            if temp_acls_method == "coldest":
+                break
+    # Grab the ACL for each chain. By default ACL of the coldest chain
+    if temp_acls_method == "coldest":
+        acls = temp_acls[:, 0]
+    else:
+        acls = numpy.max(temp_acls, axis=1)
+
+    keys = sampler.parameters + ("logl", "logp")
+    keys += sampler.blobs.dtype.names if sampler.blobs is not None else ()
+    raw = _get_raw_data(sampler, burnin_iter)
+
+    thinned = {p: [] for p in keys}
+    # Cycle over the chains, thinning them
+    for tk in range(sampler.ntemps):
+        _thinned = {p: [] for p in keys}
+
+        for ii in range(sampler.nchains):
+            for key in keys:
+                _thinned[key].append(
+                    raw[key][tk, ii, :][::-1][::acls[ii]][::-1])
+
+        for param in keys:
+            thinned[param].append(numpy.concatenate(_thinned[param]))
+    # Cast the thinned samples from a list of arrays into a 2D array for each
+    # parameter and return as a structured array
+    dtype = sampler.positions.dtype.descr + sampler.stats.dtype.descr
+    if sampler.blobs is not None:
+        dtype += sampler.blobs.dtype.descr
+    thinned_samples = numpy.zeros((sampler.ntemps, thinned[keys[0]][0].size),
+                                  dtype=numpy.dtype(dtype))
+    for param in keys:
+        thinned_samples[param] = numpy.asarray(thinned[param])
+    return thinned_samples
diff --git a/epsie/diagnostic/convergence.py b/epsie/diagnostic/convergence.py
new file mode 100644
index 00000000..8348e051
--- /dev/null
+++ b/epsie/diagnostic/convergence.py
@@ -0,0 +1,82 @@
+# Copyright (C) 2022 Richard Stiskalek, Collin Capano
+# This program is free software; you can redistribute it and/or modify it
+# under the terms of the GNU General Public License as published by the
+# Free Software Foundation; either version 3 of the License, or (at your
+# option) any later version.
+#
+# This program is distributed in the hope that it will be useful, but
+# WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General
+# Public License for more details.
+#
+# You should have received a copy of the GNU General Public License along
+# with this program; if not, write to the Free Software Foundation, Inc.,
+# 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+
+"""MCMC convergence tests."""
+
+import numpy
+from epsie.samplers import MetropolisHastingsSampler, ParallelTemperedSampler
+
+
+def gelman_rubin_test(sampler, burnin_iter):
+    """
+    Calculate the Gelman-Rubin (GR) convergence test outlined in [1] and
+    summarised in [2] for parallel, independent MCMC chains.
+
+    For a PT sampler the GR statistic is calculated for each temperature level.
+
+    Typically values of less than 1.1 or 1.2 are recommended.
+
+    Arguments
+    ---------
+    sampler : {:py:class:`epsie.sampler.MetropolisHastingsSampler`,
+               :py:class:`epsie.sampler.ParallelTemperedSampler`}
+        Epsie sampler whose samples to extract.
+    burnin_iter : int, optional
+        Number of burnin iterations to be thrown away.
+
+    Returns
+    -------
+    Rs : array
+        GR statistic of each parameter. In case of a MH sampler 1-dimensional
+        array of length `len(sampler.paramaters)` and in case of a PT sampler
+        2-dimensional array of shape `len(sampler.ntemps, len(sampler.params)`.
+
+    References
+    ----------
+    .. [1] Gelman, A. and Rubin, D.B. (1992). "Inference from Iterative
+        Simulation using Multiple Sequences". Statistical Science, 7,
+        p. 457–511.
+    .. [2] https://mc-stan.org/docs/2_18/reference-manual/
+        notation-for-samples-chains-and-draws.html
+    """
+    params = sampler.parameters
+    # Cut off burnin iterations and for PT take coldest chains
+    samples = sampler.positions[..., burnin_iter:]
+    if isinstance(sampler, MetropolisHastingsSampler):
+        return _gelman_rubin_at_temp(samples, params)
+    elif isinstance(sampler, ParallelTemperedSampler):
+        Rs = numpy.zeros((sampler.ntemps, len(params)))
+        for tk in range(sampler.ntemps):
+            Rs[tk, :] = _gelman_rubin_at_temp(samples[tk, ...], params)
+        return Rs
+    else:
+        raise ValueError("Unknown sampler type ``{}``".format(type(sampler)))
+
+
+def _gelman_rubin_at_temp(samples, params):
+    """Calculate the Gelman Rubin statistic at a given temperature level."""
+    Nchains, N = samples.shape
+    if Nchains == 1:
+        raise TypeError("GL statistic requires > 1 independent chains.")
+    # Calculate the GH statistic for each parameter independently
+    Rs = numpy.zeros(len(params))
+    for i, param in enumerate(params):
+        # Between chains variance
+        B = N * numpy.var(numpy.mean(samples[param], axis=1), ddof=1)
+        # Within chains variance
+        W = numpy.mean(numpy.var(samples[param], axis=1, ddof=1))
+        Rs[i] = ((N - 1) / N + 1 / N * B / W)**0.5
+
+    return Rs
diff --git a/epsie/samplers/ptsampler.py b/epsie/samplers/ptsampler.py
index 7df03fa1..5b1186f8 100644
--- a/epsie/samplers/ptsampler.py
+++ b/epsie/samplers/ptsampler.py
@@ -67,6 +67,7 @@ class ParallelTemperedSampler(BaseSampler):
         Specify a process pool to use for parallelization. Default is to use a
         single core.
     """
+
     def __init__(self, parameters, model, nchains, betas, swap_interval=1,
                  proposals=None, adaptive_annealer=None,
                  reset_after_swap=False, default_proposal=None,
diff --git a/test/test_diagnostics.py b/test/test_diagnostics.py
new file mode 100644
index 00000000..c49dde35
--- /dev/null
+++ b/test/test_diagnostics.py
@@ -0,0 +1,103 @@
+#!/usr/bin/env python
+
+# Copyright (C) 2020  Collin Capano
+# This program is free software; you can redistribute it and/or modify it
+# under the terms of the GNU General Public License as published by the
+# Free Software Foundation; either version 3 of the License, or (at your
+# option) any later version.
+#
+# This program is distributed in the hope that it will be useful, but
+# WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General
+# Public License for more details.
+#
+# You should have received a copy of the GNU General Public License along
+# with this program; if not, write to the Free Software Foundation, Inc.,
+# 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
+"""Performs unit tests on the ParallelTempered sampler."""
+
+import pytest
+import numpy
+from epsie import make_betas_ladder
+from epsie import diagnostic
+from _utils import Model
+
+from test_ptsampler import _create_sampler as _create_pt_sampler
+from test_mhsampler import _create_sampler as _create_mh_sampler
+
+
+NCHAINS = 5
+NTEMPS = 2
+BETAS = make_betas_ladder(NTEMPS, 1e5)
+ITERINT = 256
+SEED = 2020
+
+
+@pytest.mark.parametrize("sampler_cls", ["mh", "pt"])
+def test_thinning(sampler_cls):
+    if sampler_cls == "mh":
+        _test_mh_thinning()
+    elif sampler_cls == "pt":
+        _test_pt_thinning("coldest")
+        _test_pt_thinning("max")
+    else:
+        raise ValueError("Unknown sampler class.")
+
+
+def _test_mh_thinning():
+    model = Model()
+    sampler = _create_mh_sampler(model, nprocs=1, nchains=NCHAINS,
+                                 seed=SEED)
+    sampler.start_position = model.prior_rvs(size=NCHAINS)
+    # run both for a few iterations
+    sampler.run(ITERINT)
+
+    # Given a random seed test a comparison to a known value
+    acl = diagnostic.acl_chain(sampler.chains[0], full=True)
+    # Check that the thinnd arrays have the right shape
+    thinned = diagnostic.thinned_samples(sampler, burnin_iter=int(ITERINT/2))
+    shape = None
+    for i, param in enumerate(sampler.parameters):
+        px = thinned[param]
+        assert px.ndim == 1
+        if i == 0:
+            shape = px.shape
+        else:
+            assert px.shape == shape
+
+    # Test the GR calculation
+    Rs = diagnostic.gelman_rubin_test(
+        sampler, burnin_iter=int(ITERINT/2))
+    assert isinstance(Rs, numpy.ndarray)
+    assert Rs.ndim == 1
+    assert ~numpy.any(Rs < 1)
+
+
+def _test_pt_thinning(temp_acls_method):
+    model = Model()
+    sampler = _create_pt_sampler(model, 1, nchains=NCHAINS, betas=BETAS,
+                                 seed=SEED, swap_interval=1, proposals=None,
+                                 set_start=False)
+    sampler.start_position = model.prior_rvs(size=(NTEMPS, NCHAINS))
+
+    sampler.run(ITERINT)
+
+    thinned = diagnostic.thinned_samples(
+        sampler, burnin_iter=int(ITERINT/2), temp_acls_method=temp_acls_method)
+
+    shape = None
+    for i, param in enumerate(sampler.parameters):
+        px = thinned[param]
+        assert px.ndim == 2
+        if i == 0:
+            shape = px.shape
+        else:
+            assert px.shape == shape
+
+    # Test the GR calculation
+    Rs = diagnostic.gelman_rubin_test(
+        sampler, burnin_iter=int(ITERINT/2))
+    assert isinstance(Rs, numpy.ndarray)
+    print(Rs)
+    assert Rs.ndim == 2
+    assert ~numpy.any(Rs < 1)