Adaptive Gibbs samplers and related MCMC methods

By K. Latuszy'nski, Gareth O. Roberts, Jeffrey S. Rosenthal. 2011

87 citations recorded by the source corpus.

We consider various versions of adaptive Gibbs and Metropolis- within-Gibbs samplers, which update their selection probabilities (and per- haps also their proposal distributions) on the y during a run, by learning as they go in an attempt to optimise the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions. AMS 2000 subject classications: Primary 60J05, 65C05; secondary 62F15.

Subfields: Artificial Intelligence, Statistics and Probability, Probabilistic & Bayesian Methods

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Citations in the corpus

An Introduction to Probabilistic Programming (2018, background): “schemes to tune the standard deviation of this proposal online during sampling (Łatuszyński et al., 2013).”
Bayesian computation: a perspective on the current state, and sampling backwards and forwards (2015, methodology): “…Metropolis samplers under weak regularity conditions (Bai et al. (2011)), adaptive Gibbs and adaptive Metropolis within adaptive Gibbs samplers ((cid:32)Latuszy´nski et al. (2013)), it shows that two properties Diminishing Adaptation and Containment are suﬃcient to guarantee that an adaptive…”
Bayesian computation: a summary of the current state, and samples backwards and forwards (2015, methodology): “…et al. 2014), there are examples of seemingly reasonable adaptive algorithms that fail to converge to the intended target distribution (Bai et al. 2011; Łatuszy´nski et al. 2013), indicating that compared to standard MCMC even more care must be taken to ensure validity of inferential conclusions.”
Output-Sensitive Adaptive Metropolis-Hastings for Probabilistic Programs (2015, background): “However, provided the adaptation of the selection probabilities diminishes, with ||αt−αt−1|| → 0, then under suitable regularity conditions for the target density (see Section 4) an adaptive componentwise MH algorithm will still be ergodic [8], and the distribution on x induced by Algorithm 1 conver”