JOURNAL OF THE JAPAN STATISTICAL SOCIETY
Online ISSN : 1348-6365
Print ISSN : 1882-2754
ISSN-L : 1348-6365
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Approximation of the Meta-Analytic-Predictive Prior Distribution in the One-Way Random Effects Model with Unknown Variance
Harunori Mori
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2017 Volume 47 Issue 2 Pages 167-185

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Abstract

In order to use historical data in the design of sample surveys with a Bayesian approach, the information from the historical data must be expressed as a prior distribution. Then, the best prior distribution for the parameter of interest is a predictive distribution. The density function of the predictive distribution generally is not available in an analytical form. From the perspective of practical use, Schmidli et al. (2014) proposed an approximation for the predictive distribution using a mixture of conjugate prior distributions. Their method relies on random numbers drawn from the predictive distribution. However, if the population distribution includes a nuisance parameter, their method becomes impractical. We propose a new approximation method that does not rely on these simulated numbers. Our approximation instead minimizes the mean squared error between the exact Bayes estimator and the one corresponding to the approximated predictive distribution.

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© 2017 Japan Statistical Society
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