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Comparing Normal Random Samples, with Uncertainty About the Priors and Utilities
Author(s) -
LONGFORD NICHOLAS T.
Publication year - 2012
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00743.x
Subject(s) - prior probability , mathematics , statistics , sample size determination , bayesian probability , econometrics , sample (material) , expected value , set (abstract data type) , function (biology) , computer science , chemistry , chromatography , evolutionary biology , biology , programming language
. We study the problem of deciding which of two normal random samples, at least one of them of small size, has greater expected value. Unlike in the standard Bayesian approach, in which a single prior distribution and a single loss function are declared, we assume that a set of plausible priors and a set of plausible loss functions are elicited from the expert (the client or the sponsor of the analysis). The choice of the sample that has greater expected value is based on equilibrium priors, allowing for an impasse if for some plausible priors and loss functions choosing one and for others the other sample is associated with smaller expected loss.