Some Aspects Of Neutral To Right Priors

Abstract

Neutral to right priors are generalizations of Dirichlet process priors that fit in well with right-censored data. These priors are naturally induced by increasing processes with independent increments which, in turn, may be viewed as priors for the cumulative hazard function. This connection together with the L\'{e}vy representation of independent increment processes provides a convenient means of studying properties of \nr\ priors.

This article is a review of the theoretical aspects of \nr\ priors and provides a number of new results on their structural properties. Notable among the new results are characterizations of \nr\ priors in terms of the posterior and the cumulative hazard function. We also show that \nr\ priors are of the following nature: Consistency of Bayes' estimates implies consistency of the posterior, and posterior-consistency for complete observations automatically yields posterior-consistency for right-censored data.