Approximate Bayesian Computation for a Class of Time Series Models

TL;DR

This paper explores approximate Bayesian computation (ABC) methods tailored for time series models with intractable likelihoods, emphasizing maintaining the model's probabilistic structure for improved inference and bias analysis.

Contribution

It develops and reviews ABC-based approximation procedures for time series models, preserving the probabilistic structure and enabling bias analysis and computational adaptation.

Findings

Survey of existing ABC methods for time series

Development of novel computational approaches

Analysis of bias in ABC approximations

Abstract

In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which we mean that one cannot evaluate the likelihood even up-to a positive unbiased estimate. This paper reviews and develops a class of approximation procedures based upon the idea of ABC, but, specifically maintains the probabilistic structure of the original statistical model. This idea is useful, in that it can facilitate an analysis of the bias of the approximation and the adaptation of established computational methods for parameter inference. Several existing results in the literature are surveyed and novel developments with regards to computation are given.