Nested sampling with plateaus. (arXiv:2010.13884v2 [stat.CO] UPDATED)
<a href="http://arxiv.org/find/stat/1/au:+Fowlie_A/0/1/0/all/0/1">Andrew Fowlie</a>, <a href="http://arxiv.org/find/stat/1/au:+Handley_W/0/1/0/all/0/1">Will Handley</a>, <a href="http://arxiv.org/find/stat/1/au:+Su_L/0/1/0/all/0/1">Liangliang Su</a>
It was recently emphasised by Riley (2019); Schittenhelm & Wacker (2020) that
that in the presence of plateaus in the likelihood function nested sampling
(NS) produces faulty estimates of the evidence and posterior densities. After
informally explaining the cause of the problem, we present a modified version
of NS that handles plateaus and can be applied retrospectively to NS runs from
popular NS software using anesthetic. In the modified NS, live points in a
plateau are evicted one by one without replacement, with ordinary NS
compression of the prior volume after each eviction but taking into account the
dynamic number of live points. The live points are replenished once all points
in the plateau are removed. We demonstrate it on a number of examples. Since
the modification is simple, we propose that it becomes the canonical version of
Skilling’s NS algorithm.
It was recently emphasised by Riley (2019); Schittenhelm & Wacker (2020) that
that in the presence of plateaus in the likelihood function nested sampling
(NS) produces faulty estimates of the evidence and posterior densities. After
informally explaining the cause of the problem, we present a modified version
of NS that handles plateaus and can be applied retrospectively to NS runs from
popular NS software using anesthetic. In the modified NS, live points in a
plateau are evicted one by one without replacement, with ordinary NS
compression of the prior volume after each eviction but taking into account the
dynamic number of live points. The live points are replenished once all points
in the plateau are removed. We demonstrate it on a number of examples. Since
the modification is simple, we propose that it becomes the canonical version of
Skilling’s NS algorithm.
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