2,409 research outputs found
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
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