WIP: Improve emcee

This branch has ballooned a little as I was working on it but I think the set of features is:

• apply a minimum ln likelihood when drawing points from the prior (default leaves behaviour unchanged)
• add npool and map properties to the base_sampler
• support multiprocessing for emcee
• add new diagnostic plots, similar to the plots for ptemcee, also a plot showing how the mean and variance of the log posterior over the ensemble evolve
• calculate the burn_in using the mean and variance of the log posterior (see !842 (merged))
• use some more of the emcee moves
• port some of these changes also into kombine and ptemcee
• add periodic boundaries into ptemcee

This should probably be broken down into pieces.

cc @gregory.ashton @bruce.edelman for ptemcee and kombine.

bilby/core/sampler/base_sampler.py

@@ -88,7 +88,7 @@ class Sampler(object):
 
     """
     default_kwargs = dict()
-    npool_equiv_kwargs = ['queue_size', 'threads', 'nthreads', 'npool']
+    npool_equiv_kwargs = ['queue_size', 'threads', 'nthreads', 'npool', 'processes']
 
     def __init__(
             self, likelihood, priors, outdir='outdir', label='label',
@@ -394,7 +394,7 @@ class Sampler(object):
         else:
             return self.likelihood.log_likelihood()
 
-    def get_random_draw_from_prior(self):
+    def get_random_draw_from_prior(self, ln_l_min=-np.inf):
         """ Get a random draw from the prior distribution
 
         Returns
@@ -407,10 +407,10 @@ class Sampler(object):
         new_sample = self.priors.sample()
         draw = np.array(list(new_sample[key]
                              for key in self._search_parameter_keys))
-        self.check_draw(draw)
+        self.check_draw(draw, ln_l_min=ln_l_min)
         return draw
 
-    def get_initial_points_from_prior(self, npoints=1):
+    def get_initial_points_from_prior(self, npoints=1, ln_l_min=-np.inf):
         """ Method to draw a set of live points from the prior
 
         This iterates over draws from the prior until all the samples have a
@@ -434,17 +434,22 @@ class Sampler(object):
         unit_cube = []
         parameters = []
         likelihood = []
+
+        from tqdm import tqdm
+        bar = tqdm(total=npoints)
         while len(unit_cube) < npoints:
             unit = np.random.rand(self.ndim)
             theta = self.prior_transform(unit)
-            if self.check_draw(theta, warning=False):
+            if self.check_draw(theta, warning=False, ln_l_min=ln_l_min):
                 unit_cube.append(unit)
                 parameters.append(theta)
                 likelihood.append(self.log_likelihood(theta))
+                bar.update(n=1)
+        bar.close()
 
         return np.array(unit_cube), np.array(parameters), np.array(likelihood)
 
-    def check_draw(self, theta, warning=True):
+    def check_draw(self, theta, warning=True, ln_l_min=-np.inf):
         """
         Checks if the draw will generate an infinite prior or likelihood
 
@@ -466,10 +471,13 @@ class Sampler(object):
             if warning:
                 logger.warning('Prior draw {} has inf prior'.format(theta))
             return False
-        if abs(self.log_likelihood(theta)) in bad_values:
+        ln_l = self.log_likelihood(theta)
+        if abs(ln_l) in bad_values:
             if warning:
                 logger.warning('Prior draw {} has inf likelihood'.format(theta))
             return False
+        elif ln_l < ln_l_min:
+            return False
         return True
 
     def run_sampler(self):
@@ -539,6 +547,21 @@ class Sampler(object):
         else:
             return None
 
+    @property
+    def map(self):
+        if getattr(self, "pool", None) is not None:
+            return self.pool.map
+        else:
+            return map
+
+    @property
+    def npool(self):
+        npool = 1
+        for key in self.npool_equiv_kwargs:
+            if self.kwargs.get(key, None) is not None:
+                npool = self.kwargs[key]
+        return npool
+
 
 class NestedSampler(Sampler):
     npoints_equiv_kwargs = ['nlive', 'nlives', 'n_live_points', 'npoints', 'npoint', 'Nlive', 'num_live_points']
@@ -603,7 +626,7 @@ class NestedSampler(Sampler):
 
 
 class MCMCSampler(Sampler):
-    nwalkers_equiv_kwargs = ['nwalker', 'nwalkers', 'draws', 'Niter']
+    nwalkers_equiv_kwargs = ['nwalker', 'nwalkers', 'draws', 'Niter', 'walkers']
     nburn_equiv_kwargs = ['burn', 'nburn']
 
     def print_nburn_logging_info(self):
@@ -630,8 +653,9 @@ class MCMCSampler(Sampler):
         """
         import emcee
         try:
-            self.result.max_autocorrelation_time = int(np.max(
-                emcee.autocorr.integrated_time(samples, c=c)))
+            self.result.max_autocorrelation_time = int(np.ceil(np.max(
+                emcee.autocorr.integrated_time(samples, c=c, quiet=True, tol=10)
+            )))
             logger.info("Max autocorr time = {}".format(
                 self.result.max_autocorrelation_time))
         except emcee.autocorr.AutocorrError as e: