Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 4,  733-755

Fitting Bayesian Two-Stage Generalized Linear Models Using Random Samples via the SIR Algorithm

By

Balgobin Nandram and Erik Barry Erhardt, Worcester Polytechnic Institute,Worcester, Massachussetts, USA

SUMMARY . Although it is common practice to fit a complex Bayesian model using Markov chain Monte Carlo (MCMC) methods, we provide an alternative sampling-based method to fit a two-stage hierarchical model in which there is conjugacy conditional on the parameters in the second stage. Using the sampling importance resampling (SIR) algorithm, our method subsamples independent samples  from an approximate joint posterior density.  This is an alternative to a Metropolis-Hastings (MH) algorithm normally used to draw samples from the joint posterior density. We also provide comparison with a Metropolis (MET) algorithm. We illustrate our method using a Poisson regression model which has much interest for the analysis of rare events from small areas.  We also illustrate our method using a relatively new logistic regression model. We use four examples, three on Poisson regression and one on logistic regression, and a simulation study on the Poisson regression model to assess the performance of our method relative to the MH and the MET algorithms.

AMS (1991) subject classification.  62F15, 62J12 ;

Key words and phrases. Collapsing, conditional conjugate, hierarchical Bayesian model, MCMC monitoring, Metropolis-Hastings algorithm, Rao-Blackwellized estimator, small areas.

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