The Jeffreys-Lindley Paradox and Discovery Criteria in High Energy Physics

The Jeffreys-Lindley paradox displays how the use of a p-value (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. The setting is the test of a well-specified null hypothesis (such as the Standard Model of elementary particle physics, possibly with "nuisance parameters") versus a composite alternative (such as the Standard Model plus a new force of nature of unknown strength). The p-value, as well as the ratio of the likelihood under the null hypothesis to the maximized likelihood under the alternative, can strongly disfavor the null hypothesis, while the Bayesian posterior probability for the null hypothesis can be arbitrarily large. The academic statistics literature contains many impassioned comments on this paradox, yet there is no consensus either on its relevance to scientific communication or on its correct resolution. The paradox is quite relevant to frontier research in high energy physics. This paper is an attempt to explain the situation to both physicists and statisticians, in the hope that further progress can be made.Comment: v4: Continued editing for clarity. Figure added. v5: Minor fixes to biblio. Same as published version except for minor copy-edits, Synthese (2014). v6: fix typos, and restore garbled sentence at beginning of Sec 4 to v

Negatively Biased Relevant Subsets Induced by the Most-Powerful One-Sided Upper Confidence Limits for a Bounded Physical Parameter

Suppose an observable x is the measured value (negative or non-negative) of a true mean mu (physically non-negative) in an experiment with a Gaussian resolution function with known fixed rms deviation s. The most powerful one-sided upper confidence limit at 95% C.L. is UL = x+1.64s, which I refer to as the "original diagonal line". Perceived problems in HEP with small or non-physical upper limits for x<0 historically led, for example, to substitution of max(0,x) for x, and eventually to abandonment in the Particle Data Group's Review of Particle Physics of this diagonal line relationship between UL and x. Recently Cowan, Cranmer, Gross, and Vitells (CCGV) have advocated a concept of "power constraint" that when applied to this problem yields variants of diagonal line, including UL = max(-1,x)+1.64s. Thus it is timely to consider again what is problematic about the original diagonal line, and whether or not modifications cure these defects. In a 2002 Comment, statistician Leon Jay Gleser pointed to the literature on recognizable and relevant subsets. For upper limits given by the original diagonal line, the sample space for x has recognizable relevant subsets in which the quoted 95% C.L. is known to be negatively biased (anti-conservative) by a finite amount for all values of mu. This issue is at the heart of a dispute between Jerzy Neyman and Sir Ronald Fisher over fifty years ago, the crux of which is the relevance of pre-data coverage probabilities when making post-data inferences. The literature describes illuminating connections to Bayesian statistics as well. Methods such as that advocated by CCGV have 100% unconditional coverage for certain values of mu and hence formally evade the traditional criteria for negatively biased relevant subsets; I argue that concerns remain. Comparison with frequentist intervals advocated by Feldman and Cousins also sheds light on the issues.Comment: 22 pages, 7 figure

PhysStat-LHC Conference Summary

This timely conference in the PhyStat series brought together physicists and statisticians for talks and discussions having an emphasis on techniques for use at the Large Hadron Collider experiments. By building on the work of previous generations of experiments, and by developing common tools for comparing and combining results, we can be optimistic about our readiness for statistical analysis of the rst LHC data

Inflammation and immunity in schizophrenia: implications for pathophysiology and treatment.

Complex interactions between the immune system and the brain might have important aetiological and therapeutic implications for neuropsychiatric brain disorders. A possible association between schizophrenia and the immune system was postulated over a century ago, and is supported by epidemiological and genetic studies pointing to links with infection and inflammation. Contrary to the traditional view that the brain is an immunologically privileged site shielded behind the blood-brain barrier, studies in the past 20 years have noted complex interactions between the immune system, systemic inflammation, and the brain, which can lead to changes in mood, cognition, and behaviour. In this Review, we describe some of the important areas of research regarding innate and adaptive immune response in schizophrenia and related psychotic disorders that, we think, will be of interest to psychiatric clinicians and researchers. We discuss potential mechanisms and therapeutic implications of these findings, including studies of anti-inflammatory drugs in schizophrenia, describe areas for development, and offer testable hypotheses for future investigations

Dietary zinc deficiency increases uroguanylin accumulation in rat kidney

Dietary zinc deficiency increases uroguanylin accumulation in rat kidney.BackgroundZinc deficiency in humans produces a secretory diarrhea that is corrected by zinc supplementation. In rats, differential mRNA display analysis has shown that intestinal uroguanylin gene expression is increased in zinc deficiency. An endocrine axis involving intestinal uroguanylin and the kidney may exist. Therefore, we conducted this study to examine whether zinc deficiency would affect uroguanylin expression in the kidney of rats.MethodsA purified diet, deficient or adequate in zinc content, was fed to rats. Preprouroguanylin mRNA was localized in kidney by in situ hybridization, and prouroguanylin/uroguanylin peptides were localized in the kidney by immunohistochemistry. Abundance was measured by Western blotting and slot blotting analyses.ResultsIn situ hybridization demonstrated that preprouroguanylin mRNA-expressing cells were localized in the proximal tubules, being primarily limited to the cortical-medullary junction. Zinc deficiency did not alter the abundance or distribution of the mRNA. Immunohistochemistry, using a uroguanylin peptide-specific, affinity-purified antibody, demonstrated that immunoreactive uroguanylin peptide was localized to the same cells but that the staining was stronger in zinc-deficient rats. Western blotting analysis of kidney extracts showed that there was no difference in abundance of prouroguanylin between zinc adequate and deficient rats. However, slot blotting analysis demonstrated that the abundance of a low molecular weight immunoreactive peptide, presumably uroguanylin, was higher in extracts of zinc-deficient rats.ConclusionThe results suggest that production of prouroguanylin by the kidney, in contrast to the intestine, is not influenced by dietary zinc intake, but that higher amounts of uroguanylin in kidney extracts may reflect renal processing of the hormone obtained from the systemic circulation