Extending ABC methods to high dimensions using Gaussian Copula

Abstract

Approximate Bayesian computation (ABC) refers to a family of likelihood-free inference methods. It is usually applied in complex models in which the likelihood is either analytically unavailable or computationally intractable but forward simulation is not difficult. Conventional ABC methods such as rejection ABC can produce very good approximations to the true posterior when the problems are of low dimension. However, both the marginal posteriors and dependence structure can be poorly estimated in high-dimensional problems using conventional ABC methods. In this thesis, a Gaussian copula estimate is proposed. This method first estimates the bivariate posteriors for each pair using conventional ABC methods and then combines them together to estimate the joint posterior using a Gaussian copula. We illustrate this method with several examples.