Bayesian Nonparametric Density Estimation under Length Bias

TL;DR

This paper introduces a Bayesian nonparametric density estimation method specifically designed for length biased data, overcoming computational challenges related to normalizing constants, and demonstrating its effectiveness through simulations and real data comparisons.

Contribution

It presents a novel Bayesian nonparametric approach for length bias density estimation that avoids the normalizing constant problem, unlike previous methods.

Findings

The proposed estimator performs well in numerical simulations.

It compares favorably against the kernel density estimator for indirect data.

The method is demonstrated on real data examples.

Abstract

A density estimation method in a Bayesian nonparametric framework is presented when recorded data are not coming directly from the distribution of interest, but from a length biased version. From a Bayesian perspective, efforts to computationally evaluate posterior quantities conditionally on length biased data were hindered by the inability to circumvent the problem of a normalizing constant. In this paper we present a novel Bayesian nonparametric approach to the length bias sampling problem which circumvents the issue of the normalizing constant. Numerical illustrations as well as a real data example are presented and the estimator is compared against its frequentist counterpart, the kernel density estimator for indirect data of Jones (1991).