Presented at Int. Conf. Nuclear Data for Science and Technology, Santa Fe, Sept. 27 - Oct. 1, 2004

Probabilistic interpretation of Peelle's pertinent puzzle and its resolution

Kenneth M. Hanson, Toshihiko Kawano, and Patrick Talou
Los Alamos National Laboratory


Peelle's Pertinent Puzzle (PPP) states a seemingly plausible set of measurements with their covariance matrix, which produce an implausible answer. To answer the PPP question, we describe a reasonable experimental situation that is consistent with the PPP solution. The confusion surrounding the PPP arises in part because of its imprecise statement, which give rise to a variety of interpretations and resulting answers, some of which seem implausible. We emphasize the importance of basing the analysis on an unambiguous probabilistic model that reflects experimental situation. We present several different models of how the measurements quoted in the PPP problem could be obtained, and interpret their solution in terms of a detailed probabilistic analysis. We stress the importance of analysts having access to detailed information about experimental conditions to avoid the kind of ambiguity presented by the PPP problem.

Keywords: Peelle's pertinent puzzle, covariance matrix, strong correlation, systematic additive error, systematic normalization error, probabilistic model, Bayesian analysis, posterior distribution

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