Bayesian methods for categorical data under informative censoring

Abstract

Bayesian methods are presented for categorical sampling when some observations are censored (i.e., suffer missing distinctions between categories). Such problems have been researched over the years, as they can be important in applications. However, previous work has assumed strong restrictions, such as truthful reporting, noninformative censoring, etc.Here, we attempt to remove such restrictions. In particular, we remove two of the three restrictions imposed by Dickey, Jiang and Kanade (1987). We provide Bayesian methods for cases more general than those considered by Paulino and de B. Pereira (1992, 1995), and others. Thus, it will no longer be necessary to make unrealistic assumptions commonly employed regarding the censoring model. A theorem of Identifiability-by-Conditioning is provided, allowing familiar improper prior densities. By this theorem, we obtain identical Bayesian updating results by imposing constraints on either prior, likelihood, or posterior directly. Several computational procedures are suggested, and an example is used to illustrate methods.