Fode Zhang

Geometry of an accelerated model with censored data

From the geometrical point of view, a statistical model can be considered as a manifold with parameter plays the role of a coordinate system. In this paper, the geometrical quantities of a statistical model equipped with k-step-stress accelerated life test and progressively Type-II censoring are obtained, where censoring is allowed not only at each stress change time but also at each failure time. As an application of these quantities, the asymptotic expansions of the Bayesian prediction are investigated. Finally, some computation and simulation results are presented to illustrate our main results.

Permissible noninformative priors for the accelerated life test model with censored data

In this paper, the Jeffreys priors for the step-stress partially accelerated life test with Type-II adaptive progressive hybrid censoring scheme data are considered. Given a density function family satisfied certain regularity conditions, the Fisher information matrix and Jeffreys priors are obtained. Taking the Weibull distribution as an example, the Jeffreys priors, posterior analysis and its permissibility are discussed. The results, which present that how the accelerated stress levels, censored size, hybrid censoring time and stress change time etc. affect the Jeffreys priors, are obtained. In addition, a theorem which shows there exists a relationship between single observation and multi observations for permissible priors is proved. Finally, using Metroplis with in Gibbs sampling algorithm, these factors are confirmed by computing the frequentist coverage probabilities.

Bayesian duality and risk analysis on the statistical manifold of exponential family with censored data

Abstract Information geometry has been attracted wide attentions in the past few decades. This paper focuses on the Bayesian duality on a statistical manifold derived from the exponential family with data from life tests. Based on life testing data, the statistical manifold is constructed with a new cumulant generating function. The Bregman divergence between two parameter points is studied. The dual coordinate system and dual function are obtained. Then, the dualistic structure on the manifold is discussed. The results show that the maximum likelihood estimate can be obtained by minimizing the Bregman divergence induced from the dual function. The Bayesian analysis and prediction are investigated based on informative and non-informative priors. Consider the gamma distribution as an example, the closed-form representations of the dual coordinate system and dual function are obtained. A real data set is employed to illustrate the methodologies and experimental designs developed in this paper.