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Abstract:
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In many situations, one is interested in combining estimates from multiple sources or domains given corresponding measures of the uncertainty of each estimate. Efficient inference can be accomplished based on a hierarchical Bayesian model with appropriate priors. Such a model should take into account the uncertainty of the estimates, the uncertainty in the measures of the uncertainty, and the association between them. In this paper, a general bivariate hierarchical Bayesian model for both estimates and their corresponding measures of uncertainty is proposed. This approach can be thought of as an improvement to the general univariate hierarchical Bayesian model in terms of estimation accuracy and efficiency in the situation in which the measure and its uncertainty are correlated. We carry out Monte Carlo simulation studies to compare the performance of these two hierarchical Bayesian models under different scenarios and present estimation results. We illustrate the applications of the bivariate hierarchical Bayesian model with examples in small area estimation and brain image studies using PET data, but the model is also applicable to applications in meta-analysis and other fields.
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