INTRODUCTION

The technical feasibility of Bayesian statistics is rapidly improving as research and development activity exploits opportunities created by the computing revolution. This chapter offers an analysis and critique of Bayesian statistics, not from an internal aspect of flourishing technical development, but rather from an external aspect of the real world analyses and problem-solving tasks which the technology is designed to aid. I wish to raise for discussion the question: are the current norms and prescriptions of Bayesian statistics adequate to the tasks?

From an external standpoint, the central function of Bayesian statistics is the provision of probabilities to quantify prospective uncertainties given a current state of knowledge. The uncertainties refer to questions of fact about natural and social phenomena and about the effect of human decisions on these phenomena. The external motivation can be purely scientific, but in statistical practice there are usually decision- or policy-analytic components.

How broadly should Bayesian statistics be defined? I believe that the statistics profession has been hindered by the orthodoxy of academic mathematical statistics over the past 50 years which has largely removed evaluation of prospective uncertainties from the domain of statistical science. Thus, although statistics is the dominant source of useful probabilistic technologies, statisticians are often perceived as narrowly focused, and new professions such as “decision analysis” or “risk analysis” are created to fill the void.