Alessio Benavoli, Marco Zaffalon

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A discussion on learning and prior ignorance for sets of priors in the one-parameter exponential family

Abstract

For a conjugate likelihood-priors model in the one-parameter exponential family of distributions, we show that, by letting the parameters of the conjugate exponential prior vary in suitable sets, it is possible to define a set of conjugate priors M which guarantees prior near-ignorance without producing vacuous inferences. This result is obtained following both a behavioural and a sensitivity analysis interpretation of prior near-ignorance. We also discuss the problem of the incompatibility of learning and prior near-ignorance for sets of priors in the one-parameter exponential family of distributions in the case of imperfect observations. In particular, we prove that learning and prior near-ignorance are compatible under an imperfect observation mechanism if and only if the support of the priors in M is the whole real axis.

Keywords

Prior near-ignorance, set of distributions, exponential family of distributions, imperfect observations

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Authors’ addresses

Alessio Benavoli
Galleria 2
6928 Manno

Marco Zaffalon
Galleria 2
CH-6928 Manno
Switzerland

E-mail addresses

Alessio Benavoli		alessio@idsia.ch
Marco Zaffalon		zaffalon@idsia.ch