Improve ptemcee

This is a total rewrite of the ptemcee implementation. Originally, we had based ptemcee on emcee, but emcee has changed quite significantly and I anticipate it will be easier to maintain the two uncoupled from hereon. This adds sufficient functionality to ptemcee for it to be usable on gravitational wave events. Here is a summary of the changes

1. Add automatic convergence to the user interface: users now specify nsamples as a the primary input. The sampler will run until it has nsamples independent samples from the posterior. The user now has access to a reduced set of the ptemcee full functionality (e.g. iterations), but this isn't required given the convergence checking.
2. Add diagnostic plots for the autocorrelation time, e.g.:
3. Improve the traceplots to show the convergence and the current posterior samples
4. Add dumping of posterior samples to a .dat file
5. Add multi-processing support, tested on a 16 core machine to give a significant reduction in compute time (exact timings yet to be calculated).
6. Add regular 10-minute checkpointing

Note, I have intentionally put much of the primary logic into functions rather than class methods. This is because eventually we should port changes to parallel bilby and potentially other samplers and this is most easily done from a functional interface (at least for parallel bilby where inheritance causes issues with the parallel aspects).

bilby/core/sampler/ptemcee.py

@@ -7,6 +7,7 @@ import signal
 import sys
 import time
 import dill
+from collections import namedtuple
 
 import numpy as np
 import pandas as pd
@@ -16,6 +17,23 @@ from ..utils import logger
 from .base_sampler import SamplerError, MCMCSampler
 
 
+ConvergenceInputs = namedtuple(
+    "ConvergenceInputs",
+    [
+        "autocorr_c",
+        "autocorr_tol",
+        "autocorr_tau",
+        "safety",
+        "burn_in_nact",
+        "thin_by_nact",
+        "frac_threshold",
+        "nsamples",
+        "ignore_keys_for_tau",
+        "min_tau",
+    ],
+)
+
+
 class Ptemcee(MCMCSampler):
     """bilby wrapper ptemcee (https://github.com/willvousden/ptemcee)
 
@@ -24,101 +42,244 @@ class Ptemcee(MCMCSampler):
     documentation for that class for further help. Under Other Parameters, we
     list commonly used kwargs and the bilby defaults.
 
+    Parameters
+    ----------
+    nsamples: int, (5000)
+        The requested number of samples. Note, in cases where the
+        autocorrelation parameter is difficult to measure, it is possible to
+        end up with more than nsamples.
+    burn_in_act, thin_by_nact: int, (50, 1)
+        The number of burn-in autocorrelation times to discard and the thin-by
+        factor. Increasing burn_in_act increases the time required for burn-in.
+        Increasing thin_by_nact increases the time required to obtain nsamples.
+    autocorr_tol: int, (50)
+        The minimum number of autocorrelation times needed to trust the
+        estimate of the autocorrelation time.
+    autocorr_c: int, (5)
+        The step size for the window search used by emcee.autocorr.integrated_time
+    safety: int, (1)
+        A multiplicitive factor for the estimated autocorrelation. Useful for
+        cases where non-convergence can be observed by eye but the automated
+        tools are failing.
+    autocorr_tau:
+        The number of autocorrelation times to use in assessing if the
+        autocorrelation time is stable.
+    frac_threshold: float, (0.01)
+        The maximum fractional change in the autocorrelation for the last
+        autocorr_tau steps. If the fractional change exceeds this value,
+        sampling will continue until the estimate of the autocorrelation time
+        can be trusted.
+    min_tau: int, (1)
+        A minimum tau (autocorrelation time) to accept.
+    check_point_deltaT: float, (600)
+        The period with which to checkpoint (in seconds).
+    threads: int, (1)
+        If threads > 1, a MultiPool object is setup and used.
+    exit_code: int, (77)
+        The code on which the sampler exits.
+    store_walkers: bool (False)
+        If true, store the unthinned, unburnt chaines in the result. Note, this
+        is not recommended for cases where tau is large.
+    ignore_keys_for_tau: str
+        A pattern used to ignore keys in estimating the autocorrelation time.
+    pos0: str, list ("prior")
+        If a string, one of "prior" or "minimize". For "prior", the initial
+        positions of the sampler are drawn from the sampler. If "minimize",
+        a scipy.optimize step is applied to all parameters a number of times.
+        The walkers are then initialized from the range of values obtained.
+        If a list, for the keys in the list the optimization step is applied,
+        otherwise the initial points are drawn from the prior.
+
+
     Other Parameters
     ----------------
-    nwalkers: int, (100)
+    nwalkers: int, (200)
         The number of walkers
     nsteps: int, (100)
         The number of steps to take
-    nburn: int (50)
-        The fixed number of steps to discard as burn-in
     ntemps: int (2)
         The number of temperatures used by ptemcee
+    Tmax: float
+        The maximum temperature
 
     """
+
     # Arguments used by ptemcee
     default_kwargs = dict(
-        ntemps=20, nwalkers=200, Tmax=None, betas=None,
-        a=2.0, loglargs=[], logpargs=[], loglkwargs={},
-        logpkwargs={}, adaptation_lag=10000, adaptation_time=100, random=None,
-        adapt=False, swap_ratios=False)
-
-    def __init__(self, likelihood, priors, outdir='outdir', label='label',
-                 use_ratio=False, check_point_plot=True, skip_import_verification=False,
-                 resume=True, nsamples=5000, burn_in_nact=50, thin_by_nact=1,
-                 autocorr_c=5, safety=1, frac_threshold=0.01,
-                 autocorr_tol=50, autocorr_tau=5, min_tau=1, check_point_deltaT=600,
-                 threads=1, exit_code=77, plot=False, store_walkers=False,
-                 ignore_keys_for_tau="recalib", pos0="prior", **kwargs):
+        ntemps=20,
+        nwalkers=200,
+        Tmax=None,
+        betas=None,
+        a=2.0,
+        adaptation_lag=10000,
+        adaptation_time=100,
+        random=None,
+        adapt=True,
+        swap_ratios=False,
+    )
+
+    def __init__(
+        self,
+        likelihood,
+        priors,
+        outdir="outdir",
+        label="label",
+        use_ratio=False,
+        check_point_plot=True,
+        skip_import_verification=False,
+        resume=True,
+        nsamples=5000,
+        burn_in_nact=50,
+        thin_by_nact=1,
+        autocorr_tol=50,
+        autocorr_c=5,
+        safety=1,
+        autocorr_tau=5,
+        frac_threshold=0.01,
+        min_tau=1,
+        check_point_deltaT=600,
+        threads=1,
+        exit_code=77,
+        plot=False,
+        store_walkers=False,
+        ignore_keys_for_tau=None,
+        pos0="prior",
+        **kwargs
+    ):
         super(Ptemcee, self).__init__(
-            likelihood=likelihood, priors=priors, outdir=outdir,
-            label=label, use_ratio=use_ratio, plot=plot,
-            skip_import_verification=skip_import_verification, **kwargs)
+            likelihood=likelihood,
+            priors=priors,
+            outdir=outdir,
+            label=label,
+            use_ratio=use_ratio,
+            plot=plot,
+            skip_import_verification=skip_import_verification,
+            **kwargs
+        )
+
+        self.nwalkers = self.sampler_init_kwargs["nwalkers"]
+        self.ntemps = self.sampler_init_kwargs["ntemps"]
+        self.max_steps = 500
 
+        # Setup up signal handling
         signal.signal(signal.SIGTERM, self.write_current_state_and_exit)
         signal.signal(signal.SIGINT, self.write_current_state_and_exit)
         signal.signal(signal.SIGALRM, self.write_current_state_and_exit)
 
+        # Checkpointing inputs
+        self.exit_code = exit_code
         self.resume = resume
-        self.autocorr_c = autocorr_c
-        self.safety = safety
-        self.burn_in_nact = burn_in_nact
-        self.thin_by_nact = thin_by_nact
-        self.frac_threshold = frac_threshold
-        self.nsamples = nsamples
-        self.autocorr_tol = autocorr_tol
-        self.autocorr_tau = autocorr_tau
-        self.min_tau = min_tau
         self.check_point_deltaT = check_point_deltaT
+        self.check_point_plot = check_point_plot
+        self.resume_file = "{}/{}_checkpoint_resume.pickle".format(
+            self.outdir, self.label
+        )
+
+        # Store convergence checking inputs in a named tuple
+        convergence_inputs_dict = dict(
+            autocorr_c=autocorr_c,
+            autocorr_tol=autocorr_tol,
+            autocorr_tau=autocorr_tau,
+            safety=safety,
+            burn_in_nact=burn_in_nact,
+            thin_by_nact=thin_by_nact,
+            frac_threshold=frac_threshold,
+            nsamples=nsamples,
+            ignore_keys_for_tau=ignore_keys_for_tau,
+            min_tau=min_tau,
+        )
+        self.convergence_inputs = ConvergenceInputs(**convergence_inputs_dict)
 
+        # MultiProcessing inputs
         self.threads = threads
+
+        # Misc inputs
         self.store_walkers = store_walkers
-        self.ignore_keys_for_tau = ignore_keys_for_tau
         self.pos0 = pos0
 
-        self.check_point_plot = check_point_plot
-        self.resume_file = "{}/{}_checkpoint_resume.pickle".format(self.outdir, self.label)
-        self.exit_code = exit_code
-
     @property
     def sampler_function_kwargs(self):
-        keys = ['adapt', 'swap_ratios']
+        """ Kwargs passed to samper.sampler() """
+        keys = ["adapt", "swap_ratios"]
         return {key: self.kwargs[key] for key in keys}
 
     @property
     def sampler_init_kwargs(self):
-        return {key: value
-                for key, value in self.kwargs.items()
-                if key not in self.sampler_function_kwargs}
+        """ Kwargs passed to initialize ptemcee.Sampler() """
+        return {
+            key: value
+            for key, value in self.kwargs.items()
+            if key not in self.sampler_function_kwargs
+        }
+
+    def _translate_kwargs(self, kwargs):
+        """ Translate kwargs """
+        if "nwalkers" not in kwargs:
+            for equiv in self.nwalkers_equiv_kwargs:
+                if equiv in kwargs:
+                    kwargs["nwalkers"] = kwargs.pop(equiv)
 
     def get_pos0_from_prior(self):
-        """ for ptemcee, the pos0 has the shape ntemps, nwalkers, ndim """
+        """ Draw the initial positions from the prior
+
+        Returns
+        -------
+        pos0: list
+            The initial postitions of the walkers, with shape (ntemps, nwalkers, ndim)
+
+        """
         logger.info("Generating pos0 samples")
-        return [[self.get_random_draw_from_prior()
-                 for _ in range(self.sampler_init_kwargs["nwalkers"])]
-                for _ in range(self.kwargs['ntemps'])]
+        return [
+            [
+                self.get_random_draw_from_prior()
+                for _ in range(self.nwalkers)
+            ]
+            for _ in range(self.kwargs["ntemps"])
+        ]
 
     def get_pos0_from_minimize(self, minimize_list=None):
-        logger.info("Attempting to set pos0 from minimize")
+        """ Draw the initial positions using an initial minimization step
+
+        See pos0 in the class initialization for details.
+
+        Returns
+        -------
+        pos0: list
+            The initial postitions of the walkers, with shape (ntemps, nwalkers, ndim)
+
+        """
+
         from scipy.optimize import minimize
 
+        # Set up the minimize list: keys not in this list will have initial
+        # positions drawn from the prior
         if minimize_list is None:
             minimize_list = self.search_parameter_keys
             pos0 = np.zeros((self.kwargs["ntemps"], self.kwargs["nwalkers"], self.ndim))
         else:
             pos0 = np.array(self.get_pos0_from_prior())
 
+        logger.info("Attempting to set pos0 for {} from minimize".format(minimize_list))
+
         likelihood_copy = copy.copy(self.likelihood)
 
         def neg_log_like(params):
+            """ Internal function to minimize """
             likelihood_copy.parameters.update(
-                {key: val for key, val in zip(minimize_list, params)})
+                {key: val for key, val in zip(minimize_list, params)}
+            )
             try:
                 return -likelihood_copy.log_likelihood()
             except RuntimeError:
                 return +np.inf
-        bounds = [(self.priors[key].minimum, self.priors[key].maximum)
-                  for key in minimize_list]
+
+        # Bounds used in the minimization
+        bounds = [
+            (self.priors[key].minimum, self.priors[key].maximum)
+            for key in minimize_list
+        ]
+
+        # Run the minimization step several times to get a range of values
         trials = 0
         success = []
         while True:
@@ -126,7 +287,8 @@ class Ptemcee(MCMCSampler):
             likelihood_copy.parameters.update(draw)
             x0 = [draw[key] for key in minimize_list]
             res = minimize(
-                neg_log_like, x0, bounds=bounds, method='L-BFGS-B', tol=1e-15)
+                neg_log_like, x0, bounds=bounds, method="L-BFGS-B", tol=1e-15
+            )
             if res.success:
                 success.append(res.x)
             if trials > 100:
@@ -134,62 +296,91 @@ class Ptemcee(MCMCSampler):
             if len(success) >= 10:
                 break
 
+        # Initialize positions from the range of values
         success = np.array(success)
         for i, key in enumerate(minimize_list):
             pos0_min = np.min(success[:, i])
             pos0_max = np.max(success[:, i])
-            logger.info("Initialize {} walkers from {}->{}"
-                        .format(key, pos0_min, pos0_max))
+            logger.info(
+                "Initialize {} walkers from {}->{}".format(key, pos0_min, pos0_max)
+            )
             j = self.search_parameter_keys.index(key)
             pos0[:, :, j] = np.random.uniform(
-                pos0_min, pos0_max,
-                size=(self.kwargs["ntemps"], self.kwargs["nwalkers"]))
+                pos0_min,
+                pos0_max,
+                size=(self.kwargs["ntemps"], self.kwargs["nwalkers"]),
+            )
         return pos0
 
     def setup_sampler(self):
+        """ Either initialize the sampelr or read in the resume file """
         import ptemcee
+
         if os.path.isfile(self.resume_file) and self.resume is True:
             logger.info("Resume data {} found".format(self.resume_file))
             with open(self.resume_file, "rb") as file:
                 data = dill.load(file)
 
+            # Extract the check-point data
             self.sampler = data["sampler"]
+            self.iteration = data["iteration"]
+            self.chain_array = data["chain_array"]
+            self.log_likelihood_array = data["log_likelihood_array"]
+            self.pos0 = data["pos0"]
             self.tau_list = data["tau_list"]
             self.tau_list_n = data["tau_list_n"]
             self.time_per_check = data["time_per_check"]
 
+            # Initialize the pool
             self.sampler.pool = self.pool
             self.sampler.threads = self.threads
 
-            pos0 = None
-
-            logger.info("Resuming from previous run with time={}".format(self.sampler.time))
+            logger.info(
+                "Resuming from previous run with time={}".format(self.iteration)
+            )
 
         else:
             # Initialize the PTSampler
             if self.threads == 1:
                 self.sampler = ptemcee.Sampler(
-                    dim=self.ndim, logl=self.log_likelihood, logp=self.log_prior,
-                    **self.sampler_init_kwargs)
+                    dim=self.ndim,
+                    logl=self.log_likelihood,
+                    logp=self.log_prior,
+                    **self.sampler_init_kwargs
+                )
             else:
                 self.sampler = ptemcee.Sampler(
-                    dim=self.ndim, logl=do_nothing_function, logp=do_nothing_function,
-                    pool=self.pool, threads=self.threads, **self.sampler_init_kwargs)
+                    dim=self.ndim,
+                    logl=do_nothing_function,
+                    logp=do_nothing_function,
+                    pool=self.pool,
+                    threads=self.threads,
+                    **self.sampler_init_kwargs
+                )
 
                 self.sampler._likeprior = LikePriorEvaluator(
-                    self.search_parameter_keys, use_ratio=self.use_ratio)
+                    self.search_parameter_keys, use_ratio=self.use_ratio
+                )
 
-            # Set up empty lists
+            # Initialize storing results
+            self.iteration = 0
+            self.chain_array = self.get_zero_chain_array()
+            self.log_likelihood_array = self.get_zero_log_likelihood_array()
             self.tau_list = []
             self.tau_list_n = []
             self.time_per_check = []
+            self.pos0 = self.get_pos0()
+
+        return self.sampler
 
-            # Initialize the walker postitions
-            pos0 = self.get_pos0()
+    def get_zero_chain_array(self):
+        return np.zeros((self.nwalkers, self.max_steps, self.ndim))
 
-        return self.sampler, pos0
+    def get_zero_log_likelihood_array(self):
+        return np.zeros((self.ntemps, self.nwalkers, self.max_steps))
 
     def get_pos0(self):
+        """ Master logic for setting pos0 """
         if isinstance(self.pos0, str) and self.pos0.lower() == "prior":
             return self.get_pos0_from_prior()
         elif isinstance(self.pos0, str) and self.pos0.lower() == "minimize":
@@ -200,108 +391,61 @@ class Ptemcee(MCMCSampler):
             raise SamplerError("pos0={} not implemented".format(self.pos0))
 
     def setup_pool(self):
+        """ If threads > 1, setup a MultiPool, else run in serial mode """
         if self.threads > 1:
             import schwimmbad
+
             logger.info("Creating MultiPool with {} processes".format(self.threads))
             self.pool = schwimmbad.MultiPool(
-                self.threads,
-                initializer=init,
-                initargs=(self.likelihood, self.priors))
+                self.threads, initializer=init, initargs=(self.likelihood, self.priors)
+            )
         else:
             self.pool = None
 
     def run_sampler(self):
         self.setup_pool()
-        out = self.run_sampler_internal()
-        if self.pool:
-            self.pool.close()
-        return out
-
-    def run_sampler_internal(self):
-        import emcee
-        sampler, pos0 = self.setup_sampler()
+        sampler = self.setup_sampler()
 
         t0 = datetime.datetime.now()
         logger.info("Starting to sample")
         while True:
-            for (pos0, _, _) in sampler.sample(pos0, **self.sampler_function_kwargs):
+            for (pos0, log_posterior, log_likelihood) in sampler.sample(
+                    self.pos0, storechain=False, **self.sampler_function_kwargs):
                 pass
 
+            if self.iteration == self.chain_array.shape[1]:
+                self.chain_array = np.concatenate((
+                    self.chain_array, self.get_zero_chain_array()), axis=1)
+                self.log_likelihood_array = np.concatenate((
+                    self.log_likelihood_array, self.get_zero_log_likelihood_array()),
+                    axis=2)
+            self.pos0 = pos0
+            self.chain_array[:, self.iteration, :] = pos0[0, :, :]
+            self.log_likelihood_array[:, :, self.iteration] = log_likelihood
+
             # Calculate time per iteration
             self.time_per_check.append((datetime.datetime.now() - t0).total_seconds())
             t0 = datetime.datetime.now()
 
-            # Compute ACT tau for 0-temperature chains
-            samples = sampler.chain[0, :, : sampler.time, :]
-            taus = []
-            for ii in range(sampler.nwalkers):
-                for jj, key in enumerate(self.search_parameter_keys):
-                    if self.ignore_keys_for_tau and self.ignore_keys_for_tau in key:
-                        continue
-                    try:
-                        taus.append(
-                            emcee.autocorr.integrated_time(
-                                samples[ii, :, jj], c=self.autocorr_c, tol=0
-                            )[0]
-                        )
-                    except emcee.autocorr.AutocorrError:
-                        taus.append(np.inf)
-
-            # Apply multiplicitive safety factor
-            tau = self.safety * np.mean(taus)
-
-            # Store for convergence checking and plotting
-            self.tau_list.append(tau)
-            self.tau_list_n.append(sampler.time)
-
-            # Convert to an integer
-            tau_int = int(np.ceil(tau)) if not np.isnan(tau) else tau
-
-            if np.isnan(tau_int) or np.isinf(tau_int):
-                print_progress(
-                    self.sampler,
-                    self.time_per_check,
-                    self.nsamples,
-                    np.nan,
-                    np.nan,
-                    np.nan,
-                    [np.nan],
-                    False)
-                continue
-
-            # Calculate the effective number of samples available
-            self.nburn = int(self.burn_in_nact * tau_int)
-            self.thin = int(np.max([1, self.thin_by_nact * tau_int]))
-            samples_per_check = sampler.nwalkers / self.thin
-            self.nsamples_effective = int(sampler.nwalkers * (sampler.time - self.nburn) / self.thin)
-
-            # Calculate convergence boolean
-            converged = self.nsamples < self.nsamples_effective
-
-            # Calculate fractional change in tau from previous iterations
-            check_taus = np.array(self.tau_list[-tau_int * self.autocorr_tau:])
-            if not np.any(np.isnan(check_taus)):
-                frac = (tau - check_taus) / tau
-                tau_usable = np.all(frac < self.frac_threshold)
-            else:
-                tau_usable = False
-
-            if sampler.time < tau_int * self.autocorr_tol or tau_int < self.min_tau:
-                tau_usable = False
-
-            # Print an update on the progress
-            print_progress(
-                self.sampler,
-                self.time_per_check,
-                self.nsamples,
+            (
+                stop,
+                self.nburn,
+                self.thin,
+                self.tau_int,
                 self.nsamples_effective,
-                samples_per_check,
-                tau_int,
-                check_taus,
-                tau_usable,
+            ) = check_iteration(
+                self.chain_array[:, :self.iteration + 1, :],
+                sampler,
+                self.convergence_inputs,
+                self.search_parameter_keys,
+                self.time_per_check,
+                self.tau_list,
+                self.tau_list_n,
             )
 
-            if converged and tau_usable:
+            self.iteration += 1
+
+            if stop:
                 logger.info("Finished sampling")
                 break
 
@@ -318,11 +462,11 @@ class Ptemcee(MCMCSampler):
         self.write_current_state(plot=self.check_point_plot)
 
         # Get 0-likelihood samples and store in the result
-        samples = sampler.chain[0, :, :, :]  # nwalkers, nsteps, ndim
-        self.result.samples = (
-            samples[:, self.nburn: sampler.time:self.thin, :].reshape((-1, self.ndim)))
-        loglikelihood = sampler.loglikelihood[
-            0, :, self.nburn:sampler.time:self.thin
+        self.result.samples = self.chain_array[
+            :, self.nburn : self.iteration : self.thin, :
+        ].reshape((-1, self.ndim))
+        loglikelihood = self.log_likelihood_array[
+            0, :, self.nburn : self.iteration : self.thin
         ]  # nwalkers, nsteps
         self.result.log_likelihood_evaluations = loglikelihood.reshape((-1))
 
@@ -331,50 +475,189 @@ class Ptemcee(MCMCSampler):
         self.result.nburn = self.nburn
 
         log_evidence, log_evidence_err = compute_evidence(
-            sampler, self.outdir, self.label, self.nburn, self.thin
+            sampler, self.log_likelihood_array, self.outdir, self.label, self.nburn,
+            self.thin, self.iteration,
         )
         self.result.log_evidence = log_evidence
         self.result.log_evidence_err = log_evidence_err
 
-        self.result.sampling_time = datetime.timedelta(seconds=np.sum(self.time_per_check))
+        self.result.sampling_time = datetime.timedelta(
+            seconds=np.sum(self.time_per_check)
+        )
+
+        if self.pool:
+            self.pool.close()
 
         return self.result
 
     def write_current_state_and_exit(self, signum=None, frame=None):
         logger.warning("Run terminated with signal {}".format(signum))
-        if getattr(self, 'pool', None):
+        if getattr(self, "pool", None) or self.threads == 1:
             self.write_current_state(plot=False)
-            logger.warning("Closing pool")
+        if getattr(self, "pool", None):
+            logger.info("Closing pool")
             self.pool.close()
         sys.exit(self.exit_code)
 
     def write_current_state(self, plot=True):
-        checkpoint(self.outdir, self.label, self.nsamples_effective,
-                   self.sampler, self.nburn, self.thin,
-                   self.search_parameter_keys, self.resume_file, self.tau_list,
-                   self.tau_list_n, self.time_per_check)
+        checkpoint(
+            self.iteration,
+            self.outdir,
+            self.label,
+            self.nsamples_effective,
+            self.sampler,
+            self.nburn,
+            self.thin,
+            self.search_parameter_keys,
+            self.resume_file,
+            self.log_likelihood_array,
+            self.chain_array,
+            self.pos0,
+            self.tau_list,
+            self.tau_list_n,
+            self.time_per_check,
+        )
 
         if plot and not np.isnan(self.nburn):
             # Generate the walkers plot diagnostic
             plot_walkers(
-                self.sampler.chain[0, :, : self.sampler.time, :],
-                self.nburn, self.thin, self.search_parameter_keys, self.outdir,
-                self.label
+                self.chain_array[:, : self.iteration, :],
+                self.nburn,
+                self.thin,
+                self.search_parameter_keys,
+                self.outdir,
+                self.label,
             )
 
             # Generate the tau plot diagnostic
-            plot_tau(self.tau_list_n, self.tau_list, self.outdir, self.label,
-                     self.autocorr_tau)
+            plot_tau(
+                self.tau_list_n,
+                self.tau_list,
+                self.search_parameter_keys,
+                self.outdir,
+                self.label,
+                self.tau_int,
+                self.convergence_inputs.autocorr_tau,
+            )
+
+
+def check_iteration(
+    samples,
+    sampler,
+    convergence_inputs,
+    search_parameter_keys,
+    time_per_check,
+    tau_list,
+    tau_list_n,
+):
+    """ Per-iteration logic to calculate the convergence check
+
+    Parameters
+    ----------
+    convergence_inputs: bilby.core.sampler.ptemcee.ConvergenceInputs
+        A named tuple of the convergence checking inputs
+    search_parameter_keys: list
+        A list of the search parameter keys
+    time_per_check, tau_list, tau_list_n: list
+        Lists used for tracking the run
+
+    Returns
+    -------
+    stop: bool
+        A boolean flag, True if the stoping criteria has been met
+    burn: int
+        The number of burn-in steps to discard
+    thin: int
+        The thin-by factor to apply
+    tau_int: int
+        The integer estimated ACT
+    nsamples_effective: int
+        The effective number of samples after burning and thinning
+    """
+    import emcee
+
+    ci = convergence_inputs
+    nwalkers, iteration, ndim = samples.shape
+
+    # Compute ACT tau for 0-temperature chains
+    tau_array = np.zeros((nwalkers, ndim))
+    for ii in range(nwalkers):
+        for jj, key in enumerate(search_parameter_keys):
+            if ci.ignore_keys_for_tau and ci.ignore_keys_for_tau in key:
+                continue
+            try:
+                tau_array[ii, jj] = emcee.autocorr.integrated_time(
+                    samples[ii, :, jj], c=ci.autocorr_c, tol=0)[0]
+            except emcee.autocorr.AutocorrError:
+                tau_array[ii, jj] = np.inf
+
+    # Maximum over paramters, mean over walkers
+    tau = np.max(np.mean(tau_array, axis=0))
+
+    # Apply multiplicitive safety factor
+    tau = ci.safety * tau
+
+    # Store for convergence checking and plotting
+    tau_list.append(list(np.mean(tau_array, axis=0)))
+    tau_list_n.append(iteration)
+
+    # Convert to an integer
+    tau_int = int(np.ceil(tau)) if not np.isnan(tau) else tau
+
+    if np.isnan(tau_int) or np.isinf(tau_int):
+        print_progress(
+            iteration, sampler, time_per_check, ci.nsamples, np.nan, np.nan, np.nan, np.nan, False,
+        )
+        return False, np.nan, np.nan, np.nan, np.nan
+
+    # Calculate the effective number of samples available
+    nburn = int(ci.burn_in_nact * tau_int)
+    thin = int(np.max([1, ci.thin_by_nact * tau_int]))
+    samples_per_check = nwalkers / thin
+    nsamples_effective = int(nwalkers * (iteration - nburn) / thin)
+
+    # Calculate convergence boolean
+    converged = ci.nsamples < nsamples_effective
+
+    # Calculate fractional change in tau from previous iteration
+    check_taus = np.array(tau_list[-tau_int * ci.autocorr_tau :])
+    taus_per_parameter = check_taus[-1, :]
+    if not np.any(np.isnan(check_taus)):
+        frac = (taus_per_parameter - check_taus) / taus_per_parameter
+        max_frac = np.max(frac)
+        tau_usable = np.all(frac < ci.frac_threshold)
+    else:
+        max_frac = np.nan
+        tau_usable = False
+
+    if iteration < tau_int * ci.autocorr_tol or tau_int < ci.min_tau:
+        tau_usable = False
+
+    # Print an update on the progress
+    print_progress(
+        iteration,
+        sampler,
+        time_per_check,
+        ci.nsamples,
+        nsamples_effective,
+        samples_per_check,
+        tau_int,
+        max_frac,
+        tau_usable,
+    )
+    stop = converged and tau_usable
+    return stop, nburn, thin, tau_int, nsamples_effective
 
 
 def print_progress(
+    iteration,
     sampler,
     time_per_check,
     nsamples,
     nsamples_effective,
     samples_per_check,
     tau_int,
-    tau_list,
+    max_frac,
     tau_usable,
 ):
     # Setup acceptance string
@@ -388,9 +671,7 @@ def print_progress(
     )
 
     ave_time_per_check = np.mean(time_per_check[-3:])
-    time_left = (
-        (nsamples - nsamples_effective) * ave_time_per_check / samples_per_check
-    )
+    time_left = (nsamples - nsamples_effective) * ave_time_per_check / samples_per_check
     if time_left > 0:
         time_left = str(datetime.timedelta(seconds=int(time_left)))
     else:
@@ -398,7 +679,10 @@ def print_progress(
 
     sampling_time = datetime.timedelta(seconds=np.sum(time_per_check))
 
-    tau_str = "{}:{:0.1f}->{:0.1f}".format(tau_int, np.min(tau_list), np.max(tau_list))
+    if max_frac >= 0:
+        tau_str = "{}(+{:0.1f})".format(tau_int, max_frac)
+    else:
+        tau_str = "{}({:0.1f})".format(tau_int, max_frac)
     if tau_usable:
         tau_str = "={}".format(tau_str)
     else:
@@ -406,13 +690,13 @@ def print_progress(
 
     evals_per_check = sampler.nwalkers * sampler.ntemps
 
-    ncalls = "{:1.1e}".format(sampler.time * sampler.nwalkers * sampler.ntemps)
+    ncalls = "{:1.1e}".format(iteration * sampler.nwalkers * sampler.ntemps)
     eval_timing = "{:1.1f}ms/ev".format(1e3 * ave_time_per_check / evals_per_check)
     samp_timing = "{:1.1f}ms/sm".format(1e3 * ave_time_per_check / samples_per_check)
 
     print(
         "{}| {} | nc:{}| a0:{}| swp:{}| n:{}<{}| tau{}| {}| {}".format(
-            sampler.time,
+            iteration,
             str(sampling_time).split(".")[0],
             ncalls,
             acceptance_str,
@@ -427,16 +711,30 @@ def print_progress(
     )
 
 
-def checkpoint(outdir, label, nsamples_effective, sampler, nburn, thin,
-               search_parameter_keys, resume_file, tau_list, tau_list_n,
-               time_per_check):
+def checkpoint(
+    iteration,
+    outdir,
+    label,
+    nsamples_effective,
+    sampler,
+    nburn,
+    thin,
+    search_parameter_keys,
+    resume_file,
+    log_likelihood_array,
+    chain_array,
+    pos0,
+    tau_list,
+    tau_list_n,
+    time_per_check,
+):
     logger.info("Writing checkpoint and diagnostics")
     ndim = sampler.dim
 
     # Store the samples if possible
     if nsamples_effective > 0:
         filename = "{}/{}_samples.txt".format(outdir, label)
-        samples = sampler.chain[0, :, nburn:sampler.time:thin, :].reshape(
+        samples = np.array(chain_array)[:, nburn : iteration : thin, :].reshape(
             (-1, ndim)
         )
         df = pd.DataFrame(samples, columns=search_parameter_keys)
@@ -445,14 +743,17 @@ def checkpoint(outdir, label, nsamples_effective, sampler, nburn, thin,
     # Pickle the resume artefacts
     sampler_copy = copy.copy(sampler)
     del sampler_copy.pool
-    sampler_copy._chain = sampler._chain[:, :, : sampler.time, :]
-    sampler_copy._logposterior = sampler._logposterior[:, :, : sampler.time]
-    sampler_copy._loglikelihood = sampler._loglikelihood[:, :, : sampler.time]
-    sampler_copy._beta_history = sampler._beta_history[:, : sampler.time]
 
     data = dict(
-        sampler=sampler_copy, tau_list=tau_list, tau_list_n=tau_list_n,
-        time_per_check=time_per_check)
+        iteration=iteration,
+        sampler=sampler_copy,
+        tau_list=tau_list,
+        tau_list_n=tau_list_n,
+        time_per_check=time_per_check,
+        log_likelihood_array=log_likelihood_array,
+       chain_array=chain_array,
+        pos0=pos0,
+    )
 
     with open(resume_file, "wb") as file:
         dill.dump(data, file, protocol=4)
@@ -465,16 +766,24 @@ def plot_walkers(walkers, nburn, thin, parameter_labels, outdir, label):
     nwalkers, nsteps, ndim = walkers.shape
     idxs = np.arange(nsteps)
     fig, axes = plt.subplots(nrows=ndim, ncols=2, figsize=(8, 3 * ndim))
-    scatter_kwargs = dict(lw=0, marker="o", markersize=1)
+    scatter_kwargs = dict(lw=0, marker="o", markersize=1, alpha=0.05,)
     # Plot the burn-in
     for i, (ax, axh) in enumerate(axes):
         ax.plot(
-            idxs[: nburn + 1], walkers[:, : nburn + 1, i].T, color="C1", **scatter_kwargs
+            idxs[: nburn + 1],
+            walkers[:, : nburn + 1, i].T,
+            color="C1",
+            **scatter_kwargs
         )
 
     # Plot the thinned posterior samples
     for i, (ax, axh) in enumerate(axes):
-        ax.plot(idxs[nburn::thin], walkers[:, nburn::thin, i].T, color="C0", **scatter_kwargs)
+        ax.plot(
+            idxs[nburn::thin],
+            walkers[:, nburn::thin, i].T,
+            color="C0",
+            **scatter_kwargs
+        )
         axh.hist(walkers[:, nburn::thin, i].reshape((-1)), bins=50, alpha=0.8)
         axh.set_xlabel(parameter_labels[i])
         ax.set_ylabel(parameter_labels[i])
@@ -485,24 +794,26 @@ def plot_walkers(walkers, nburn, thin, parameter_labels, outdir, label):
     plt.close(fig)
 
 
-def plot_tau(tau_list_n, tau_list, outdir, label, autocorr_tau):
+def plot_tau(
+    tau_list_n, tau_list, search_parameter_keys, outdir, label, tau, autocorr_tau
+):
     fig, ax = plt.subplots()
-    ax.plot(tau_list_n, tau_list, "-", color='C1')
-    check_tau_idx = -int(tau_list[-1] * autocorr_tau)
-    check_taus = tau_list[check_tau_idx:]
-    check_taus_n = tau_list_n[check_tau_idx:]
-    ax.plot(check_taus_n, check_taus, "-", color='C0')
+    for i, key in enumerate(search_parameter_keys):
+        ax.plot(tau_list_n, np.array(tau_list)[:, i], label=key)
+    ax.axvline(tau_list_n[-1] - tau * autocorr_tau)
     ax.set_xlabel("Iteration")
     ax.set_ylabel(r"$\langle \tau \rangle$")
+    ax.legend()
     fig.savefig("{}/{}_checkpoint_tau.png".format(outdir, label))
     plt.close(fig)
 
 
-def compute_evidence(sampler, outdir, label, nburn, thin, make_plots=True):
+def compute_evidence(sampler, log_likelihood_array, outdir, label, nburn, thin,
+                     iteration, make_plots=True):
     """ Computes the evidence using thermodynamic integration """
     betas = sampler.betas
     # We compute the evidence without the burnin samples, but we do not thin
-    lnlike = sampler.loglikelihood[:, :, nburn:sampler.time]
+    lnlike = log_likelihood_array[:, :, nburn : iteration]
     mean_lnlikes = np.mean(np.mean(lnlike, axis=1), axis=1)
 
     mean_lnlikes = mean_lnlikes[::-1]
@@ -535,8 +846,7 @@ def compute_evidence(sampler, outdir, label, nburn, thin, make_plots=True):
 
         ax2.semilogx(min_betas, evidence, "-o")
         ax2.set_ylabel(
-            r"$\int_{\beta_{min}}^{\beta=1}"
-            + r"\langle \log(\mathcal{L})\rangle d\beta$",
+            r"$\int_{\beta_{min}}^{\beta=1}" + r"\langle \log(\mathcal{L})\rangle d\beta$",
             size=16,
         )
         ax2.set_xlabel(r"$\beta_{min}$")
@@ -590,14 +900,14 @@ class LikePriorEvaluator(object):
     def __call__(self, x):
         lp = self.logp(x)
         if np.isnan(lp):
-            raise ValueError('Prior function returned NaN.')
+            raise ValueError("Prior function returned NaN.")
 
-        if lp == float('-inf'):
+        if lp == float("-inf"):
             # Can't return -inf, since this messes with beta=0 behaviour.
             ll = 0
         else:
             ll = self.logl(x)
             if np.isnan(ll).any():
-                raise ValueError('Log likelihood function returned NaN.')
+                raise ValueError("Log likelihood function returned NaN.")
 
         return ll, lp