Rare event ABC-SMC$^{2}$

TL;DR

This paper introduces a novel rare event ABC-SMC$^{2}$ algorithm that improves high-dimensional Bayesian inference by combining rare event SMC with an SMC$^{2}$ framework, reducing tuning and computational challenges.

Contribution

It extends the rare event ABC approach within an SMC$^{2}$ algorithm, offering a more efficient and less tuned alternative to previous MCMC-based methods.

Findings

The new method performs well on toy and real-world network models.

It requires less tuning than MCMC-based ABC methods.

Demonstrates improved scalability for high-dimensional data.

Abstract

Approximate Bayesian computation (ABC) is a well-established family of Monte Carlo methods for performing approximate Bayesian inference in the case where an ``implicit'' model is used for the data: when the data model can be simulated, but the likelihood cannot easily be pointwise evaluated. A fundamental property of standard ABC approaches is that the number of Monte Carlo points required to achieve a given accuracy scales exponentially with the dimension of the data. Prangle et al. (2018) proposes a Markov chain Monte Carlo (MCMC) method that uses a rare event sequential Monte Carlo (SMC) approach to estimating the ABC likelihood that avoids this exponential scaling, and thus allows ABC to be used on higher dimensional data. This paper builds on the work of Prangle et al. (2018) by using the rare event SMC approach within an SMC algorithm, instead of within an MCMC algorithm. The new method has a similar structure to SMC$^{2}$ (Chopin et al., 2013), and requires less tuning than the MCMC approach. We demonstrate the new approach, compared to existing ABC-SMC methods, on a toy example and on a duplication-divergence random graph model used for modelling protein interaction networks.