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Objective Bayesian Inference for a Generalized Marginal Random Effects Model
Physikalisch-Technische Bundesanstalt, Berlin, Gremany.ORCID iD: 0000-0003-1359-3311
Physikalisch-Technische Bundesanstalt, Berlin, Germany.
Physikalisch-Technische Bundesanstalt, Berlin, Germany.
2016 (English)In: Bayesian Analysis, ISSN 1936-0975, E-ISSN 1931-6690, Vol. 11, no 1, p. 25-45Article in journal (Refereed) Published
Abstract [en]

An objective Bayesian inference is proposed for the generalized marginal random effects model p(x|μ, σλ) = f((x − μ1) T (V + σ2 λI) −1 (x − μ1))/ det(V + σ2 λI). 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.

Place, publisher, year, edition, pages
International Society for Bayesian Analysis , 2016. Vol. 11, no 1, p. 25-45
Keywords [en]
Objective Bayesian inference, reference prior, random effects model
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:oru:diva-76709DOI: 10.1214/14-BA933ISI: 000372068400002Scopus ID: 2-s2.0-84957591748OAI: oai:DiVA.org:oru-76709DiVA, id: diva2:1354108
Available from: 2019-09-24 Created: 2019-09-24 Last updated: 2019-10-25

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Bodnar, Olha

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