Informational Dynamics of Censored Observations

The analysis of stochastic models is often greatly complicated if there are censored observations of the random variables. This paper characterizes families of distributions which help keep tractable the analysis of such models. Our primary motivation is to provide guidance to practitioners in the selection of distributions: If a modeler feels that no member of the families we characterize is a reasonable approximation, then he will almost surely encounter serious analytic and computational problems if his data include censored observations. We characterize a family of distributions for which there exist fixed-dimensional sufficient statistics of purely censored observations. We also characterize an important subset of this family, appropriate for situations where data include both censored and exact observations. We derive the corresponding predictive distributions using arbitrary priors and present some general results relating stochastic dominance among predictive distributions to the parameters of the prior. We also analyze the cases of discrete and mixed random variables.