Isaiah Good

“We can judge of the perfection to which a science has come by the facility, more or less great, with which it may be approached by calculation.”Quetelet (1828), as quoted by Landau & Lazarsfeld in theInternational Encyclopedia of Statistics(p. 828).Suppose that some event F occurs and later an event E either occurs or does not. I am going to talk aboutthe extent to whichFtends to causeE, orthe causal propensityof Eprovided byF, orthe propensity or tendency of F to causeE, denoted by Q(E:F). For example, F might be the event that the captain of a firing squad shouts “Fire” and E might be that the shootee's life is_ Ended (F for Fire, E for Ended). The negation of E is denoted by E, which in this example means that the shootee does not drop dead.

This paper attempts to define Exploratory Data Analysis (EDA) more precisely than usual, and to produce the beginnings of a philosophy of this topical and somewhat novel branch of statistics. A data set is, roughly speaking, a collection of k-tuples for some k. In both descriptive statistics and in EDA, these k-tuples, or functions of them, are represented in a manner matched to human and computer abilities with a view to finding patterns that are not "kinkera". A kinkus is a pattern that has a negligible probability of being even partly potentially explicable. A potentially explicable pattern is one for which there probably exists a hypothesis of adequate "explicativity", which is another technical probabilistic concept. A pattern can be judged to be probably potentially explicable even if we cannot find an explanation. The theory of probability understood here is one of partially ordered (interval-valued), subjective (personal) probabilities. Among other topics relevant to a philosophy of EDA are the "reduction" of data; Francis Bacon's philosophy of science; the automatic formulation of hypotheses; successive deepening of hypotheses; neurophysiology; and rationality of type II