Likelihood should be strictly increasing?
Hi @joshspeagle I came across some weird behaviour which I think is down to `dynesty` accepting new points based on the condition `logl >= loglstar`, e.g., https://github.com/joshspeagle/dynesty/blob/master/dynesty/sampler.py#L393.

My understanding of the NS algorithm was that the likelihood needs to be strictly increasing, I think that this means the correct condition is `logl > loglstar`.
diff --git a/dynesty/sampler.py b/dynesty/sampler.py
index 6af7d3d..5bebdcd 100644
--- a/dynesty/sampler.py
+++ b/dynesty/sampler.py
@@ -305,7 +305,7 @@ class Sampler(object):
             # If we've already update our bounds, check if we've exceeded the
             # saved log-likelihood threshold. (This is useful when sampling
             # within `dynamicsampler`).
-            return loglstar >= self.logl_first_update
+            return loglstar > self.logl_first_update
 
     def _empty_queue(self):
         """Dump all live point proposals currently on the queue."""
@@ -390,7 +390,7 @@ class Sampler(object):
                 self.update_proposal(blob)
 
             # If we satisfy the log-likelihood constraint, we're done!
-            if logl >= loglstar:
+            if logl > loglstar:
                 break
 
             # If there has been more than `update_interval` function calls
diff --git a/dynesty/sampling.py b/dynesty/sampling.py
index 6ff8136..96a8854 100644
--- a/dynesty/sampling.py
+++ b/dynesty/sampling.py
@@ -223,7 +223,7 @@ def sample_rwalk(args):
         # Check proposed point.
         v_prop = prior_transform(np.array(u_prop))
         logl_prop = loglikelihood(np.array(v_prop))
-        if logl_prop >= loglstar:
+        if logl_prop > loglstar:
             u = u_prop
             v = v_prop
             logl = logl_prop
@@ -379,7 +379,7 @@ def sample_rstagger(args):
         # Check proposed point.
         v_prop = prior_transform(np.array(u_prop))
         logl_prop = loglikelihood(np.array(v_prop))
-        if logl_prop >= loglstar:
+        if logl_prop > loglstar:
             u = u_prop
             v = v_prop
             logl = logl_prop
@@ -516,7 +516,7 @@ def sample_slice(args):
             nexpand += 1
 
             # "Stepping out" the left and right bounds.
-            while logl_l >= loglstar:
+            while logl_l > loglstar:
                 u_l -= axis
                 if unitcheck(u_l, nonperiodic):
                     v_l = prior_transform(np.array(u_l))
@@ -525,7 +525,7 @@ def sample_slice(args):
                     logl_l = -np.inf
                 nc += 1
                 nexpand += 1
-            while logl_r >= loglstar:
+            while logl_r > loglstar:
                 u_r += axis
                 if unitcheck(u_r, nonperiodic):
                     v_r = prior_transform(np.array(u_r))
@@ -569,7 +569,7 @@ def sample_slice(args):
                 ncontract += 1
 
                 # If we succeed, move to the new position.
-                if logl_prop >= loglstar:
+                if logl_prop > loglstar:
                     fscale.append(window / axlen)
                     u = u_prop
                     break
@@ -705,7 +705,7 @@ def sample_rslice(args):
         nexpand += 1
 
         # "Stepping out" the left and right bounds.
-        while logl_l >= loglstar:
+        while logl_l > loglstar:
             u_l -= axis
             if unitcheck(u_l, nonperiodic):
                 v_l = prior_transform(np.array(u_l))
@@ -714,7 +714,7 @@ def sample_rslice(args):
                 logl_l = -np.inf
             nc += 1
             nexpand += 1
-        while logl_r >= loglstar:
+        while logl_r > loglstar:
             u_r += axis
             if unitcheck(u_r, nonperiodic):
                 v_r = prior_transform(np.array(u_r))
@@ -758,7 +758,7 @@ def sample_rslice(args):
             ncontract += 1
 
             # If we succeed, move to the new position.
-            if logl_prop >= loglstar:
+            if logl_prop > loglstar:
                 fscale.append(window / axlen)
                 u = u_prop
                 break
@@ -1209,7 +1209,7 @@ def sample_hslice(args):
             nc += 1
             ncontract += 1
             # If we succeed, move to the new position.
-            if logl_prop >= loglstar:
+            if logl_prop > loglstar:
                 u = u_prop
                 break
             # If we fail, check if the new point is to the left/right of
['dynesty/sampler.py', 'dynesty/sampling.py']