Stat Colloquium [In-person]: Dr. Sanjay Chaudhuri

Title: On an Empirical Likelihood-Based Solution to Approximate Bayesian Computation Problem

Abstract:

For many complex models studied in natural, engineering, and environmental sciences, it is nearly impossible to specify a likelihood for the observed data.  Approximate Bayesian Computation (ABC) methods try to estimate such model parameters only by comparing the given observation and some replicates generated from the model for various input parameter values. No explicit relationship between the parameters and the data is postulated.  In this article, we propose an empirical likelihood (EL) based solution to the ABC problem. By construction, our method is based on an interpretable likelihood (i.e. the EL) which is computed using estimating equations completely specified by the observed and the replicated data and a few well-chosen summary statistics.  The proposed method can be justified through information projections on a specified class of densities.  We further show that the posterior is consistent and discuss several of its favourable large sample and large replication properties.  Illustrative examples from various real-life applications will also be presented.       

This work is joint with Subhroshekhar Ghosh and Pham Thi Kim Cuc all from the National University of Singapore.

Keywords: ABC; Empirical likelihood; Data-dependent estimating equations; Modified empirical likelihood.