Prior Bayes: Rubin’s View of Statistics

Introduction

What is statistics? The common way of looking at it is a collection of methods, somehow or other produced, and one should use one of those methods for a given set of data. The typical user who has little more than this comes to a statistician asking for THE answer, as if the data are sufficient to get this without knowing the problem.

No; the first thing is to formulate the problem. One cannot do better than to assume that there is an unknown state of nature, that there is a probability distribution of observations given a state of nature, a set of possible actions, and that each action in each state of nature has (possibly random) consequences.

Following the von (1944) axioms for utility, in 1947 (see Rubin 1987a) I was able to show that if one has a self-consistent evaluation of actions in each state of nature, the utility function for an unknown state of nature has to be an integral of the utilities for the states of nature. Another way of looking at this in the...