Bayesian nonparametric density estimation under length bias

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 article, we present a novel Bayesian nonparametric approach to the length bias sampling problem that 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.