Bayesian Conditionalization Research Articles

Bayesian Personalism, Falsificationism, and the Problem of Induction

The practical problem of induction is that of how to modify preexisting expectations about the future in the light of incoming evidence. There is nothing in Hume's arguments to prevent there being a uniquely rational recipe for doing this. The Bayesians claim to have found such a recipe in Bayesian Conditionalization. Bayesian personalists claim that the rationality of this recipe solves the practical problem of induction, which arises in everyday life, and in statistical and scientific inference, and quite possibly the sceptical problem as well. I defend this solution against some standard traditional sceptical arguments concerning induction, and against falsificationist criticisms. I also defend it against a new species of scepticism, about the rationality of acting so as to maximize one's own expected utility function, due to David Miller.

Bayesian Conditionalisation and the Principle of Minimum Information

The use of the principle of minimum information, or equivalently the principle of maximum entropy, has been advocated by a number of authors over recent years both in statistical physics as well as more generally in statistical inference.' It has perhaps not been sufficiently appreciated by philosophers, however, that this principle, when properly understood, affords a rule of inductive inference of the widest generality.2 The purpose of this paper is to draw attention to the generality of the principle. Thus the Bayesian rule of conditionalisation, as well as its extension by R. C. Jeffrey, will be exhibited as special cases. General conditions under which it yields a unique prescription will also be studied. Detailed treatment will be restricted to the finite-dimensional case but an outline of the general case is given in the Appendix. The underlying idea of maximum entropy inference is this. Suppose P to be a probability distribution assigning probabilities px, ..., p, to n mutually exclusive and jointly exhaustive events. Then the information-theoretic entropy of the distribution is defined by