Sequential Monte Carlo ABC: an overview with application to COVID-19 data

In modern Bayesian analysis, we often encounter cases where the likelihood function either lacks an analytic form or becomes computationally intensive due to the complexity of the model. This study provides an overview of approximate Bayesian computation (ABC), a simulation-based approach to Bayesian inference that circumvents the need to evaluate the likelihood function. We begin with a concise explanation of the fundamental principles underlying ABC, followed by an introduction to various ABC algorithms guidance on selecting simulation parameters. Our focus is on ABC using a sequential Monte Carlo method, which offers an efficient means for parameter estimation and model selection. We demonstrate the application of algorithms combining ABC and sequential Monte Carlo through multiple examples, including their adaptation to time-dependent susceptible-infected-removed epidemic models. We conclude with a discussion on potential future research directions in ABC algorithms.