Bayesian statistics

Abstract

In interpreting crystallographic results there are generally two sources of information: the exueriment itself and data from previous investigations: Conventional statistics does not provide a simple, conceptually clear means of combining these. Bayesian statistics does, however, provide such a framework. To illustrqte this '"e consider procedures for estimating a diffraction peak's intensity from its measured profile.Various methods have been proposed for doing this. Howeve:t; all ignore some of the available information, thereby reducing the accuracy of the estimation. Moreover, some make assumptions about structure present in the sequence of counts and so produce a large positive bias in the estimates of weak reflections. We present a profile fitting approach based upon the Bayesian three-stage regression model, which we believe overcomes these failings. He discuss the underlying theory, describe briefly its implementation for off-line data reduction, and report on its application to various protein data sets.