A rare event approach to high dimensional Approximate Bayesian computation

TL;DR

This paper introduces RE-ABC, a novel high-dimensional Approximate Bayesian Computation method leveraging rare event techniques and latent variable models to improve inference efficiency and accuracy.

Contribution

The paper proposes a new RE-ABC method that uses rare event estimation and latent variables, reducing computational cost in high-dimensional settings.

Findings

RE-ABC has lower computational cost than standard ABC in high dimensions

RE-ABC provides more accurate inference without extensive dimension reduction

Empirical results demonstrate effectiveness in Gaussian and infectious disease models

Abstract

Approximate Bayesian computation (ABC) methods permit approximate inference for intractable likelihoods when it is possible to simulate from the model. However they perform poorly for high dimensional data, and in practice must usually be used in conjunction with dimension reduction methods, resulting in a loss of accuracy which is hard to quantify or control. We propose a new ABC method for high dimensional data based on rare event methods which we refer to as RE-ABC. This uses a latent variable representation of the model. For a given parameter value, we estimate the probability of the rare event that the latent variables correspond to data roughly consistent with the observations. This is performed using sequential Monte Carlo and slice sampling to systematically search the space of latent variables. In contrast standard ABC can be viewed as using a more naive Monte Carlo estimate. We use our rare event probability estimator as a likelihood estimate within the pseudo-marginal Metropolis-Hastings algorithm for parameter inference. We provide asymptotics showing that RE-ABC has a lower computational cost for high dimensional data than standard ABC methods. We also illustrate our approach empirically, on a Gaussian distribution and an application in infectious disease modelling.