Priors for Exponential Families Which Maximize the Association between Past and Future Observations

Donato M. Cifarelli and Eugenio Regazzini
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Donato M. Cifarelli: Università L. Bocconi, Istituto Metodi Quantitativi
Eugenio Regazzini: Università degli Studi, Dipartimento di Matematica

A chapter in Probability and Bayesian Statistics, 1987, pp 83-95 from Springer

Abstract: Abstract Throughout the present paper, {Xn} denotes a sequence of random quantities which are regarded as exchangeable, and which are assessed with a probability measure P(•) which is a member of the mixture-exponential family. To be precise, it will be presumed that the assessment P(•) for any finite subsequence (X1,…,Xn) can be represented using the product of an identical non-degenerate parametric measure for each Xi, Pθ (•)= P(•θ=θ), determined by (1.1) $$ {\rm{d}}{{\rm{P}}_{\rm{\theta }}} = \exp \{ {\rm{\theta x}} - {\rm{M}}({\rm{\theta }})\} {\rm{d\mu }} $$ μ being a σ-finite measure on the class B of Borel sets of IR. It will always be assumed that the interior X° of the convex hull X of the support of μ (in symbols:suρp(μ))is a nonempty open set (interval) in IR and that {Pθ;θεΘ} is a regular exponential family (cf. Barndorff - Nielsen 1978, p.116). The latter condition implies that Θ = {θ:M(θ)

Keywords: conjugate prior; de Finetti’s coherent probabilities; (regular) exponential families; finitely additive probabilities; noninformative priors (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4613-1885-9_9

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