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Objective Bayesian point and region estimation in location-scale models.

José M. Bernardo (2007)

SORT

Point and region estimation may both be described as specific decision problems. In point estimation, the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this...

On maximum entropy priors and a most likely likelihood in auditing.

Agustín Hernández Bastida, María del C. Martel Escobar, Francisco José Vázquez Polo (1998)

Qüestiió

There are two basic questions auditors and accountants must consider when developing test and estimation applications using Bayes' Theorem: What prior probability function should be used and what likelihood function should be used. In this paper we propose to use a maximum entropy prior probability function MEP with the most likely likelihood function MLL in the Quasi-Bayesian QB model introduced by McCray (1984). It is defined on an adequate parameter. Thus procedure only needs an expected value...

On optimal credibility premiums in multiperiod insurance

W. Antoniak, M. Kałuszka (2014)

Applicationes Mathematicae

This paper focuses on the problem of optimal arrangement of a stream of premiums in a multiperiod credibility model. On the basis of a given claim history (screening) and some individual information unknown to the insurance company (signaling), we derive the optimal streams in the case when the coverage period is not necessarily fixed, e.g., because of lapses, renewals, deaths, total losses, etc.

On the foundations of statistics and decision theory.

José M. Bernardo, Javier Girón (1983)

Trabajos de Estadística e Investigación Operativa

An elementary axiomatic foundation for decision theory is presented at a general enough level to cover standard applications of Bayesian methods. The intuitive meaning of both axioms and results is stressed. It is argued that statistical inference is a particular decision problem to which the axiomatic argument fully applies.

Optimal alternative robustness in Bayesian Decision Theory.

Fabrizio Ruggeri, Jacinto Martín, David Ríos Insua (2003)

RACSAM

In Martin et al (2003), we suggested an approach to general robustness studies in Bayesian Decision Theory and Inference, based on ε-contamination neighborhoods. In this note, we generalise the results considering neighborhoods based on norms, specifically, the supremum norm for utilities and the total variation norm for probability distributions. We provide tools to detect changes in preferences between alternatives under perturbations of the prior and/or the utility and the most sensitive direction....

Optimal sequential multiple hypothesis tests

Andrey Novikov (2009)

Kybernetika

This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized.

Optimal sequential procedures with Bayes decision rules

Andrey Novikov (2010)

Kybernetika

In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect...

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