Displaying similar documents to “A note on an open problem in the foundations of statistics.”

Quasi-Bayesian behaviour: a more realistic approach to decision making?

Francisco Javier Girón, Sixto Ríos (1980)

Trabajos de Estadística e Investigación Operativa

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In this paper the theoretical and practical implications of dropping -from the basic Bayesian coherence principles- the assumption of comparability of every pair of acts is examined. The resulting theory is shown to be still perfectly coherent and has Bayesian theory as a particular case. In particular we question the need of weakening or ruling out some of the axioms that constitute the coherence principles; what are their practical implications; how this drive to the notion of partial...

Optimal alternative robustness in Bayesian Decision Theory.

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

RACSAM

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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...

On the foundations of statistics and decision theory.

José M. Bernardo, Javier Girón (1983)

Trabajos de Estadística e Investigación Operativa

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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.

Foundations of subjective probability and decision making: Discussion.

Irving John Good, Ludovico Piccinato, Cesáreo Villegas, James M. Dickey, Morris H. DeGroot, Donald A. S. Fraser, Simon French, Dennis V. Lindley (1980)

Trabajos de Estadística e Investigación Operativa

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Discussion on the papers by Girón, F. J. and Ríos, S., Quasi-Bayesian behaviour: a more realistic approach to dicision making? and by Hill, B. M., On finite additivity, non-conglomerability and statistical paradoxes, both of them part of a round table on Foundations of Subjective Probability and Decision Making held in the First International Congress on Bayesian Methods (Valencia, Spain, 28 May - 2 June 1979).

Robust inference in probability under vague information.

Giuliana Regoli (1996)

Mathware and Soft Computing

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Vague information can be represented as comparison of previsions or comparison of probabilities, and a robust analysis can be done, in order to make inference about some quantity of interest and to measure the imprecision of the answers. In particular, in some decision problems the answer can be unique.

Local and regional coherence utility assessment procedures.

Melvin R. Novick, D. F. Dekeyrel, D. T. Chuang (1980)

Trabajos de Estadística e Investigación Operativa

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Novick and Lindley (1978, 1979) have dealt with the use of utility functions for applications in education and have advocated the use of the standard gamble (von Neumann and Morgenstern, 1953) elicitation procedure with the addition of coherence checking using overspecification and a least squares fit. In this procedure utilities are inferred from probability judgements offered by the assessor. This paper describes local and regional coherence procedures which seek utility coherence...

Personal and inter-personal ethics: Discussion.

Dennis V. Lindley, Allan M. Skene, José M. Bernardo, Morris H. DeGroot, Irving John Good, Anthony O'Hagan (1980)

Trabajos de Estadística e Investigación Operativa

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Discussion on the papers by Savage, I. Richard, On not being rational and by Kadane, Joseph B. and Sedransj, Nell, Toward a more ethical clinical trial, both of them part of a round table on Personal and inter-personal ethics held in the First International Congress on Bayesian Methods (Valencia, Spain, 28 May - 2 June 1979).