Delayed acceptance ABC-SMC

TL;DR

This paper introduces a delayed acceptance ABC-SMC method that uses a cheap, approximate simulator to efficiently explore parameter space, reducing the need for expensive true simulations in complex Bayesian inference tasks.

Contribution

It develops a novel delayed acceptance MCMC within ABC-SMC framework that automates the use of approximate simulators to improve computational efficiency.

Findings

Effective reduction in computational cost for ABC inference

Automatic tuning with minimal parameters required

Successful application to complex stochastic models

Abstract

Approximate Bayesian computation (ABC) is now an established technique for statistical inference used in cases where the likelihood function is computationally expensive or not available. It relies on the use of a~model that is specified in the form of a~simulator, and approximates the likelihood at a~parameter value $\theta$ by simulating auxiliary data sets $x$ and evaluating the distance of $x$ from the true data $y$. However, ABC is not computationally feasible in cases where using the simulator for each $\theta$ is very expensive. This paper investigates this situation in cases where a~cheap, but approximate, simulator is available. The approach is to employ delayed acceptance Markov chain Monte Carlo (MCMC) within an ABC sequential Monte Carlo (SMC) sampler in order to, in a~first stage of the kernel, use the cheap simulator to rule out parts of the parameter space that are not worth exploring, so that the ``true'' simulator is only run (in the second stage of the kernel) where there is a~reasonable chance of accepting proposed values of $\theta$. We show that this approach can be used quite automatically, with few tuning parameters. Applications to stochastic differential equation models and latent doubly intractable distributions are presented.