Foundations for direct inference (Q2266302)

''Direct inference'' is the form of uncertain inference that proceeds from a premise that concerns a statistical distribution in a population to a conclusion about an individual or a sample from that population. It is contrasted with ''inverse inference'', which is the inference from the characteristics of a sample to a distribution in a population. The latter has been the subject of controversy for many years, while the former has been regarded as fairly unproblematic. It is coming to be recognized that while we tend to agree on when direct inference is warranted, formulating the principles according to which it should proceed is not at all easy. The present paper represents an attempt to derive a reasonable set of principles for direct inference from two epistemological principles - an acceptance rule, and an ''undercutting defeater'' rule. Whether the attempt is altogether successful, or whether the rules derived are altogether reasonable, will remain controversial. Nevertheless, the paper is enlightening, and a number of important and relatively unknown issues are raised. The framework is that of ''nomic probability'', characterized in terms of a possible world semantics. This will be more convenient for philosophers and logicians than for statisticians. The issues raised, however, are precisely ones that statisticians should attend to.