Approximate Bayesian Computational Methods for the Inference of Unknown Parameters

Abstract

Recent advances in biology, economics, engineering and physical sciences have generated a large number of mathematical models for describing the dynamics of complex systems. A key step in mathematical modelling is to estimate model parameters in order to realize experimental observations. However, it is difficult to derive the analytical density functions in the Bayesian methods for these mathematical models. During the last decade, approximate Bayesian computation (ABC) has been developed as a major method for the inference of parameters in mathematical models. A number of new methods have been designed to improve the efficiency and accuracy of ABC. Theoretical studies have also been conducted to investigate the convergence property of these methods. In addition, these methods have been applied to a wide range of deterministic and stochastic models. This chapter gives a brief review of the main ABC algorithms and various improvements.