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Testing Hardy–Weinberg equilibrium: An objective Bayesian analysis
Author(s) -
Consonni Guido,
Moreno El�as,
Venturini Sergio
Publication year - 2010
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4084
Subject(s) - prior probability , bayesian probability , robustness (evolution) , mathematics , class (philosophy) , statistical hypothesis testing , posterior probability , sample size determination , stability (learning theory) , econometrics , mathematical economics , computer science , statistics , artificial intelligence , machine learning , biochemistry , chemistry , gene
We analyze the general (multiallelic) Hardy–Weinberg equilibrium problem from an objective Bayesian testing standpoint. We argue that for small or moderate sample sizes the answer is rather sensitive to the prior chosen, and this suggests to carry out a sensitivity analysis with respect to the prior. This goal is achieved through the identification of a class of priors specifically designed for this testing problem. In this paper, we consider the class of intrinsic priors under the full model, indexed by a tuning quantity, the training sample size. These priors are objective, satisfy Savage's continuity condition and have proved to behave extremely well for many statistical testing problems. We compute the posterior probability of the Hardy–Weinberg equilibrium model for the class of intrinsic priors, assess robustness over the range of plausible answers, as well as stability of the decision in favor of either hypothesis. Copyright © 2010 John Wiley & Sons, Ltd.