This paper introduces measures of information for Bayesian analysis when the support of data distribution is truncated progressively. The focus is on the lifetime distributions where the support is truncated at the current age t>=0. Notions of uncertainty and information are presented and operationalized by Shannon entropy, Kullback-Leibler information, and mutual information. Dynamic updatings...

This paper illustrates a sequential method to detect significant parameter changes for time series models. Rather than relying on an explicit state equation, the parameters’ dynamics are assessed as a change-point problem by combining Bayesian estimation with a nonparametric test of hypothesis. The Kullback-Leibler divergence between the posterior probability densities given two different sets ...

Frailty has been introduced as a group-wise random effect to describe the within-group dependence for correlated survival data. In this article, we propose a penalized joint likelihood method for nonparametric estimation of hazard function. With the proposed method, the frailty variance component and the smoothing parameters become the tuning parameters that are selected to minimize a loss func...