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March 2022 Finding our Way in the Dark: Approximate MCMC for Approximate Bayesian Methods
Evgeny Levi, Radu V. Craiu
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Bayesian Anal. 17(1): 193-221 (March 2022). DOI: 10.1214/20-BA1250

Abstract

With larger data at their disposal, scientists are emboldened to tackle complex questions that require sophisticated statistical models. It is not unusual for the latter to have likelihood functions that elude analytical formulations. Even under such adversity, when one can simulate from the sampling distribution, Bayesian analysis can be conducted using approximate methods such as Approximate Bayesian Computation (ABC) or Bayesian Synthetic Likelihood (BSL). A significant drawback of these methods is that the number of required simulations can be prohibitively large, thus severely limiting their scope. In this paper we design perturbed MCMC samplers that can be used within the ABC and BSL paradigms to significantly accelerate computation while maintaining control on computational efficiency. The proposed strategy relies on recycling samples from the chain’s past. The algorithmic design is supported by a theoretical analysis while practical performance is examined via a series of simulation examples and data analyses.

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Evgeny Levi. Radu V. Craiu. "Finding our Way in the Dark: Approximate MCMC for Approximate Bayesian Methods." Bayesian Anal. 17 (1) 193 - 221, March 2022. https://doi.org/10.1214/20-BA1250

Information

Published: March 2022
First available in Project Euclid: 9 December 2020

Digital Object Identifier: 10.1214/20-BA1250

Subjects:
Primary: 60K35 , 62-08
Secondary: 60J22

Keywords: Approximate Bayesian Computation , k-Nearest Neighbour , Perturbed MCMC , synthetic likelihood

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Vol.17 • No. 1 • March 2022
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