Likelihood Distributions in Nuclear Physics
In most data analyses, the normal (Gaussian) distribution is assumed to appropriately characterize the likelihood, that is, the conditional probability of each measurement, given an assumed value, p(measurement | assumed value). On the other hand, there is ample evidence in nuclear physics of significant disagreements among measurements, which are inconsistent with the normal distribution, given their stated uncertainties. In this study the histories of measurements of the lifetimes of several particles are examined to determine what can be inferred about the distribution of their values relative to their stated uncertainties. These data strongly support using a Student t distribution for the shape of the likelihood function over a Gaussian. Furthermore, experimenters tend to underestimate the systematic uncertainties in their results. It is shown that analyses based on long-tailed likelihoods, like the t distribution, gracefully cope with outlying data.