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March 2016 Objective Bayesian Inference for a Generalized Marginal Random Effects Model
O. Bodnar, A. Link, C. Elster
Bayesian Anal. 11(1): 25-45 (March 2016). DOI: 10.1214/14-BA933

Abstract

An objective Bayesian inference is proposed for the generalized marginal random effects model p(x|μ,σλ)=f((xμ1)T(V+σλ2I)1(xμ1))/det(V+σλ2I). The matrix V is assumed to be known, and the goal is to infer μ given the observations x=(x1,,xn)T, while σλ is a nuisance parameter. In metrology this model has been applied for the adjustment of inconsistent data x1,,xn, where the matrix V contains the uncertainties quoted for x1,,xn.

We show that the reference prior for grouping {μ,σλ} is given by π(μ,σλ)F22, where F22 denotes the lower right element of the Fisher information matrix F. We give an explicit expression for the reference prior, and we also prove propriety of the resulting posterior as well as the existence of mean and variance of the marginal posterior for μ. Under the additional assumption of normality, we relate the resulting reference analysis to that known for the conventional balanced random effects model in the asymptotic case when the number of repeated within-class observations for that model tends to infinity.

We investigate the frequentist properties of the proposed inference for the generalized marginal random effects model through simulations, and we also study its robustness when the underlying distributional assumptions are violated. Finally, we apply the model to the adjustment of current measurements of the Planck constant.

Citation

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O. Bodnar. A. Link. C. Elster. "Objective Bayesian Inference for a Generalized Marginal Random Effects Model." Bayesian Anal. 11 (1) 25 - 45, March 2016. https://doi.org/10.1214/14-BA933

Information

Published: March 2016
First available in Project Euclid: 4 February 2015

zbMATH: 1357.62103
MathSciNet: MR3447090
Digital Object Identifier: 10.1214/14-BA933

Keywords: objective Bayesian inference , random effects model , reference prior

Rights: Copyright © 2016 International Society for Bayesian Analysis

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Vol.11 • No. 1 • March 2016
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