Objective Single-Case Probabilities and the Foundations of Statistics

Publisher Summary This chapter discusses single-case probabilities and the foundations of statistics. The shortcomings of frequency interpretations are summarized, thus providing a basis for judging the advantages of a propensity interpretation. The single-case propensity interpretation is introduced, paying particular attention to the indeterministic nature of propensities. Next it is shown that the relation between propensities and frequencies makes the existence of propensities incompatible with a Humean metaphysics and epistemology. The chapter explains how a single-case propensity interpretation may illuminate typical examples of statistical practice. A single-case propensity interpretation provides an extremely natural understanding of the standard formalism for dealing with series of trials. Indeed, it provides a natural interpretation for the whole mathematical theory of probability and statistics.