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\iteman{ZMATH 1237.62004}
\itemau{Benavoli, Alessio; Zaffalon, Marco}
\itemti{A model of prior ignorance for inferences in the one-parameter exponential family.}
\itemso{J. Stat. Plann. Inference 142, No. 7, 1960-1979 (2012).}
\itemab
Summary: This paper proposes a model of prior ignorance about a scalar variable based on a set of distributions $\cal M$. In particular, a set of minimal properties that a set $\cal M$ of distributions should satisfy to be a model of prior ignorance without producing vacuous inferences is defined. In the case the likelihood model corresponds to a one-parameter exponential family of distributions, it is shown that the above minimal properties are equivalent to a special choice of the domains for the parameters of the conjugate exponential prior. This makes it possible to define the largest (that is, the least-committal) set of conjugate priors $\cal M$ that satisfies the above properties. The obtained set $\cal M$ is a model of prior ignorance with respect to the functions (queries) that are commonly used for statistical inferences; it is easy to elicit and, because of conjugacy, tractable; and encompasses frequentist and the so-called objective Bayesian inferences with improper priors. An application of the model to a problem of inference with count data is presented.
\itemrv{~}
\itemcc{62A01 62F15 65C60}
\itemut{lower and upper expectations}
\itemli{doi:10.1016/j.jspi.2012.01.023}
\end