Inverse Regression and Approximate Bayesian Computation

Abstract

Approximate Bayesian Computation (ABC) is an approach that allows summary statistics to be used to estimate parameters in statistical models. An attractive aspect of ABC is that it allows interpretable summary statistics such as moments and quantiles to be used to estimate a parameter for which standard estimators exist only in numeric form. In the first part of the talk, I will review ABC, and discuss how inverse regression can be used to construct interpretable estimators based on sample quantiles. Examples in which two regression indices outperform a single index highlight the advantage of using inverse regression in this application. Then, we apply the inverse regression/ABC method to two concrete problems. First, we consider the multivariate structure of ancestry-informative gene expression markers. Second, we consider the problem of estimating the distribution of glomerular radii based on needle biopsies of kidney tissue.?