Bayesian nonparametric density estimation for doubly-truncated data

摘要

A Bayesian nonparametric density estimator is presented for doubly-truncated data. The estimator is based on a Pólya tree prior, and readily extended to truncated regression. The approach nicely blends a standard parametric normal fit with the nonparametric maximum likelihood estimator. Since the density is directly modeled, a standard likelihood approach applies; inference is efficiently obtained through an adaptiveMarkov chain Monte Carlo and no manual tuning is required. The estimator is broadly illustrated on simulated data, the quasar luminosity data of Efron and Petrosian (1999), times of cancer diagnosis considered in Moreira and U?a-álvarez (2012), and the AIDS induction time data of Lagakos, Barraj, and De Gruttola (1988).