Functional regression approximate Bayesian computation for Gaussian process density estimation

TL;DR

This paper introduces a new Bayesian nonparametric approach for hierarchical density estimation using Gaussian processes and approximate Bayesian computation, enabling effective borrowing of strength across related groups.

Contribution

It develops a hierarchical prior for density functions with a novel functional regression adjustment within ABC, advancing nonparametric Bayesian inference methods.

Findings

Demonstrates improved density estimation in simulations

Successfully applied to Brazilian high school exam data

Shows effective hierarchical modeling of related densities

Abstract

We propose a novel Bayesian nonparametric method for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a major challenge in this context. To address this problem, we introduce a hierarchically structured prior, defined over a set of univariate density functions, using convenient transformations of Gaussian processes. Inference is performed through approximate Bayesian computation (ABC), via a novel functional regression adjustment. The performance of the proposed method is illustrated via a simulation study and an analysis of rural high school exam performance in Brazil.