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Theory of Probability and Mathematical Statistics

Non-informative bayesian inference for heterogeneity in a generalized marginal random effects meta-analysis]

O. Bodnar

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Abstract: In this paper an objective Bayesian inference is proposed for the heterogeneity parameter in a generalized marginal random effects model. Models of this kind are widely used in meta-analysis and in inter-laboratory comparisons. Under the assumption of elliptically contoured distributions, a reference prior for the model parameters is obtained and the analytical expression of the corresponding posterior is derived. We also state necessary conditions for the resulting posterior to be proper and for the existence of its first two moments. The obtained general theoretical results are illustrated for three popular families of elliptically contoured distributions: normal distribution, t-distribution, and Laplace distribution.

Keywords: Non-informative prior, generalized random effects model, meta-analysis, estimation of heterogeneity, elliptically contoured distribution.

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