Dynamic Display of Changing Posterior in Bayesian Survival Analysis
We consider the problem of estimating an unknown distribution function F in the presence of censoring under the conditions that a parametric model is believed to hold approximately. We use a Bayesian approach, in which the prior on F is a mixture of Dirichlet distributions. A hyperparameter of the prior determines the extent to which this prior concentrates its mass around the parametric family. A Gibbs sampling algorithm to estimate the posterior distributions of the parameters of interest is reviewed. An importance sampling scheme enables us to use the output of the Gibbs sampler to very quickly recalculate the posterior when we change the hyperparameters of the prior. The calculations can be done sufficiently fast to enable the dynamic display of the changing posterior as the prior hyperparameters are varied.
KeywordsMarkov Chain Posterior Distribution Conditional Distribution Importance Sampling Borel Subset
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