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The JeffreysLindley Paradox and Discovery Criteria in High Energy Physics
, 2014
"... The Jeffreys–Lindley paradox displays how the use of a pvalue (or number of standard deviations z) in a frequentist hypothesis test can lead to an inference that is radically different from that of a Bayesian hypothesis test in the form advocated by Harold Jeffreys in the 1930s and common today. Th ..."
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The Jeffreys–Lindley paradox displays how the use of a pvalue (or number of standard deviations z) in a frequentist hypothesis test can lead to an inference that is radically different from that of a Bayesian hypothesis test in the form advocated by Harold Jeffreys in the 1930s and common today
Appendix: the JeffreysLindley paradox and its relevance to statistical testing
"... The purpose of this technical appendix is to present a formal statement of the JereysLindley paradox, which I alluded to in the main text of this lecture in Section 7.1, and to explain subsequent developments in Bayesian statistical methodology that resolve the paradox. The resolution requires a ch ..."
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The purpose of this technical appendix is to present a formal statement of the JereysLindley paradox, which I alluded to in the main text of this lecture in Section 7.1, and to explain subsequent developments in Bayesian statistical methodology that resolve the paradox. The resolution requires a
Test manuscript No. (will be inserted by the editor) Combining Bayesian procedures for testing
, 2009
"... Abstract Jeffreys and PereiraStern Bayesian procedures for testing provide measures of evidence in favour the null hypothesis which can lead to different decisions. We introduce two procedures for testing based on pooling the posterior evidences in favour of the null hypothesis provided by these pr ..."
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by these procedures. We prove that the proposed procedure which has been built using the linear pool of probability is a Bayes test and does not lead to JeffreysLindley paradox. We apply the results for testing precise hypothesis about parameters of some asymmetric family of distributions including the skew
Submitted APPROXIMATION OF IMPROPER PRIOR BY VAGUE
"... Abstract. We propose a convergence mode for prior distributions which allows a sequence of probability measures to have an improper limiting measure. We define a sequence of vague priors as a sequence of probability measures that converges to a noninformative prior. We consider some cases where vag ..."
Submitted to Journal of Scientific Exploration RESPONSE TO DOBYNS
"... Abstract. Dobyns ’ article suggests some reasons why orthodox statistics might be superior to Bayesian statistics when discussing random event generator statistics. Several of his main arguments are examined and discussed. Introduction. I became interested in this topic when, after joining the Socie ..."
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the Society for Scientific Exploration, I ordered the back issues of the Journal for Scientific Exploration and set about reading them. While studying the paper of Jahn et. al. (1987) I noticed that it actually provided a nice reallife example of the JeffreysLindley paradox. It also made me ask
Testing Hypotheses in Particle Physics: Plots of p0 Versus p1
, 2014
"... For situations where we are trying to decide which of two hypotheses H0 and H1 provides a better description of some data, we discuss the usefulness of plots of p0 versus p1, where pi is the pvalue for testing Hi. They provide an interesting way of understanding the difference between the standard ..."
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way of excluding H1 and the CLs approach; the Punzi definition of sensitivity; the relationship between pvalues and likelihood ratios; and the probability of observing misleading evidence. They also help illustrate the Law of the Iterated Logarithm and the JeffreysLindley paradox. 1
CONSISTENCY OF BAYESIAN PROCEDURES FOR VARIABLE SELECTION
"... It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, i ..."
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that the Jeffreys–Lindley paradox refers to the wellknown fact that a point null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity. This implies that some limiting forms of proper prior distributions are not necessarily suitable for testing
Consistency of Bayes factors for intrinsic priors in normal linear models
"... Abstract The JeffreysLindley paradox refers to the wellknown fact that a sharp null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity, thus implying that the resulting Bayesian procedure is not consistent, and that some limiting f ..."
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Abstract The JeffreysLindley paradox refers to the wellknown fact that a sharp null hypothesis on the normal mean parameter is always accepted when the variance of the conjugate prior goes to infinity, thus implying that the resulting Bayesian procedure is not consistent, and that some limiting
Lindley’s paradox
 Journal of the American Statistical Society 77
, 1982
"... A sharp null hypothesis may be strongly rejected by a standard samplingtheory test of significance and yet be awarded high odds by a Bayesian analysis based on a small prior probability for the null hypothesis and a diffuse distribution of one’s remaining probability over the alternative hypothesis ..."
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hypothesis. This disagreement between samplingtheory and Bayesian methods was first studied by Harold Jeffreys (1939), and it was first called a paradox by Dennis Lindley (1957). The paradox can be exhibited in the simple case where we are testing θ = 0 using a single observation Y from a normal
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