Approximating Interval hypothesis : p-values and Bayes factors
Rousseau, Judith (2007), Approximating Interval hypothesis : p-values and Bayes factors, in Bernardo, J.M.; Bayarri, M.J.; Berger, J.O.; Dawid, A.P.; Heckerman, D.; Smith, A.F.M.; West, M., Bayesian Statistics 8 Proceedings of the Eighth Valencia International Meeting June 2–6, 2006, Oxford University Press : Oxford, p. 417-452
TypeCommunication / Conférence
Conference titleValencia International Meeting on Bayesian Statistics 2006
Book titleBayesian Statistics 8 Proceedings of the Eighth Valencia International Meeting June 2–6, 2006
Book authorBernardo, J.M.; Bayarri, M.J.; Berger, J.O.; Dawid, A.P.; Heckerman, D.; Smith, A.F.M.; West, M.
Number of pages688
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Abstract (EN)In this paper we study Bayes factors and special p-values in their capacity of approximating interval null hypotheses (or more generally neighbourhoods of point null) hypotheses by point null or eventually parametric families in the case of the goodness of ﬁt test of a parametric family. We prove that when the number of observations is large Bayes factors for point null hypotheses can approximate Bayes factors for interval null hypotheses for extremely small intervals. We also interpret the signiﬁcance of calibration goodness of ﬁt tests using a p-value in terms of width of neighbourhoods of the point null hypothesis. Finally we study the consistency of Bayes factors for goodness of ﬁt tests of parametric families, which enables us to shed light on the behaviour of the Bayes factors.
Subjects / KeywordsAsymptotic; Bayes factors; Point null; P-values; Goodness of fit tests
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