Some Aspects Of Neutral To Right Priors

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 Lévy representation of independent increment processes provides a convenient means of studying properties of neutral to right priors.
This article is a review of the theoretical aspects of neutral to right priors and provides a number of new results on their structural properties. Notable among the new results are characterizations of neutral to right priors in terms of the posterior and the cumulative hazard function. We also show that neutral to right 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.