Believable Statements of Uncertainty and Believable Science.

Nearly fifty years ago, two landmark papers appeared that should have cured the problem of ambiguous uncertainty statements in published data. Eisenhart's paper in called for statistically meaningful numbers, and Currie's paper revealed the wide range in common definitions of detection limit. Confusion and worse can result when uncertainties are misinterpreted or ignored. The recent stories of cold fusion, variable radioactive decay, and piezonuclear reactions provide cautionary examples in which prior probability has been neglected. We show examples from our laboratory and others to illustrate the fact that uncertainty depends on both statistical and scientific judgment.