Marginal sequential Monte Carlo for doubly intractable models

TL;DR

This paper introduces a flexible sequential Monte Carlo method for Bayesian inference in doubly intractable models, improving likelihood estimates adaptively and comparing its performance with existing algorithms like ABC.

Contribution

It proposes new SMC samplers with alternative distribution sequences and adaptive likelihood estimation, extending prior methods focused mainly on data-point tempering.

Findings

The proposed method improves likelihood estimation accuracy.

It demonstrates competitive performance against ABC and other existing algorithms.

Adaptive strategies enhance convergence and efficiency.

Abstract

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte Carlo techniques (M{\o}ller et al., 2006; Murray et al., 2006) for tackling this problem; these approaches being members of the more general class of pseudo-marginal, or exact-approximate, Monte Carlo algorithms (Andrieu and Roberts, 2009), which make use of unbiased estimates of intractable posteriors. Everitt et al. (2017) investigated the use of exact-approximate importance sampling (IS) and sequential Monte Carlo (SMC) in doubly intractable problems, but focussed only on SMC algorithms that used data-point tempering. This paper describes SMC samplers that may use alternative sequences of distributions, and describes ways in which likelihood estimates may be improved adaptively as the algorithm progresses, building on ideas from Moores et al. (2015). This approach is compared with a number of alternative algorithms for doubly intractable problems, including approximate Bayesian computation (ABC), which we show is closely related to the method of M{\o}ller et al. (2006).