A Theory of Bayesian Data Analysis

Bayesian data analysis is concerned with the type of data manipulations, transformations, and just plain playing with the data, that any serious scientist engages in during the statistical or other analysis of his data. It is largely a post-data procedure, rather than a pre-data procedure, since even when it is desirable to think through such matters quite carefully prior to obtaining the data, in many real world experiments time and other constraints would provide limits on such activities. Compare Hacking or the discussion in Hodges concerning how much is enough. Bayesian data analysis goes beyond the mere data manipulations, however, and attempts to integrate the theory of subjective probability with such data analysis. In this respect it differs from other data-analytic approaches, which appear, more or less, to abandon probability. In this article the author attempts further to elucidate the theory of Bayesian data analysis begun in Hill. kr