Bayesian Estimation of a Weibull Distribution in a Highly Censored and Small Sample Setting

Mostafa Bacha 1 Gilles Celeux 1
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive
Abstract : We propose and investigate through Monte Carlo simulations two methods for Bayesian inference for the shape and the scale parameters of a Weibull distribution in a small and highly censored sample setting. The first method, WLB-SIR, is the Sampling Importance Resampling-adjusted Weighted Likelihood Bootstrap of Newton and Raftery. The second one is a new Bayesian Restoration Maximization BRM new algorithm working along the same line but replacing the bootstrap weighting step by a stochastic simulation step of the censored failure times. The advantage of the BRM method is that it takes account of the prior distribution in its first step. As a consequence, the Sampling Importance Resampling-adjusted version of BRM, BRM-SIR, is less fragile than WLB-SIR as it appears from our numerical experiments for Weibull parameters estimation. This article also includes a flexible procedure to transform prior knowledge into prior distributions on the Weibull parameters.
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[Research Report] RR-2993, INRIA. 1996
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Mostafa Bacha, Gilles Celeux. Bayesian Estimation of a Weibull Distribution in a Highly Censored and Small Sample Setting. [Research Report] RR-2993, INRIA. 1996. 〈inria-00073704〉

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