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A conservative prior for bayesian hierarchical models in biostatistics Hossain, Md. Shahadut

Abstract

Hierarchical models are suitable and very natural to model many real life phenomena, where data arise in nested fashion. The use of Bayesian approach to hierarchical models has numerous advantages over the classical approach. Estimating a phenomenon with hierarchical model can be viewed as a smoothing problem, and hence while summarizing such a phenomenon via hierarchical model we do not want to undersmooth the phenomenon. That is, in most of the practical applications undersmoothing is more serious type of error than oversmoothing. So, we need an estimation approach which can guard against undersmoothing. If we can control the undersmoothing reasonably, we may get a better calibrated summary of the phenomenon we estimate. In this study, we have incorporated the aspect of smoothing in estimating the parameters of Bayesian hierarchical models. In doing so we have proposed a conservative prior for the variance component to achieve the adequate degree of smoothness while estimating the phenomenon under study. We have conducted simulation studies to decide about the appropriate values to be used for the hyperparameter while using the conservative prior to ensure the adequate degree of smoothness. We have investigated the performance of the proposed conservative prior in guarding against undersmoothing in simple normal-normal hierarchical models (random effects models for normal response) and in non-parametric regression curve estimation problem via simulation studies. We have also investigated the performance of the proposed prior compared to those of the uniform shrinkage prior and the Jeffreys' prior, with respect to both guarding against undersmoothing and the MSE of the estimated model parameters, through simulation studies.

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