Peelle’s Pertinent Puzzle and its Solution

¹ Institut für Hochenergiephysik der ÖAW, Nikolsdorfer Gasse 18, 1050 Wien, Austria
² Atominstitut, Technische Universität Wien, Wiedner Hauptstraße 8–10, 1040 Wien, Austria

^a e-mail: rudolf.fruehwirth@oeaw.ac.at
^b e-mail: dn@kph.tuwien.ac.at
^c e-mail: leeb@kph.tuwien.ac.at

Abstract

Peelle’s Pertinent Puzzle is a long-standing problem of nuclear data evaluation. In principle it is a phenomenon exhibiting unexpected mean values for experimental data affected by statistical and systematic errors. This occurs for non-linear functions of statistical quantities, e.g. for a product, but not for a sum. In the literature on nuclear data, this phenomenon was attributed to the underlying non-linearity of the relation between data. Here, we show in terms of Bayesian Statistics that Peelle’s Pertinent Puzzle is primarily caused by improper estimates of covariance matrices of experiments and not exclusively by non-linearities. Applying the correct covariance matrix leads to the exact posterior expectation value and variance for an arbitrary number of uncorrelated measurement points which are normalized by the same quantity. It is also shown that the mean value converges in probability to zero with increasing number of observations, if the improper covariance matrix is applied.