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

@@ -49,9 +49,9 @@ class Ptemcee(MCMCSampler):
         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)
+    burn_in_nact, 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.
+        factor. Increasing burn_in_nact 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
@@ -130,8 +130,8 @@ class Ptemcee(MCMCSampler):
         skip_import_verification=False,
         resume=True,
         nsamples=5000,
-        burn_in_nact=50,
-        thin_by_nact=1,
+        burn_in_nact=10,
+        thin_by_nact=0.5,
         autocorr_tol=50,
         autocorr_c=5,
         safety=1,
@@ -892,7 +892,12 @@ def init(likelihood_in, priors_in):
 
 class LikePriorEvaluator(object):
     """
-    A overwrite of the ptemcee.LikePriorEvaluator to use bilby likelihood and priors
+    This class is copied and modified from ptemcee.LikePriorEvaluator, see
+    https://github.com/willvousden/ptemcee for the original version
+
+    We overwrite the logl and logp methods in order to improve the performance
+    when using a MultiPool object: essentially reducing the amount of data
+    transfer overhead.
 
     """