The idea that perceptual and cognitive systems must incorporate knowledge about the structure of the environment has become a central dogma of cognitive theory. In a Bayesian context, this idea is often realized in terms of “tuning the prior”—widely assumed to mean adjusting prior probabilities so that they match the frequencies of events in the world. This kind of “ecological” tuning has often been held up as an ideal of inference, in fact defining an “ideal observer.” But widespread as this (...) viewpoint is, it directly contradicts Bayesian philosophy of probability, which views probabilities as degrees of belief rather than relative frequencies, and explicitly denies that they are objective characteristics of the world. Moreover, tuning the prior to observed environmental frequencies is subject to overfitting, meaning in this context overtuning to the environment, which leads (ironically) to poor performance in future encounters with the same environment. Whenever there is uncertainty about the environment—which there almost always is—an agent's prior should be biased away from ecological relative frequencies and toward simpler and more entropic priors. (shrink)

In 1866, the young John Venn published The Logic of Chance, motivated largely by the desire to correct what he saw as deep fallacies in the reasoning of historical determinists such as Henry Buckle and in the optimistic heralding of a true social science by Adolphe Quetelet. Venn accepted the inevitable determinism implied by the physical sciences, but denied that the stable social statistics cited by Buckle and Quetelet implied a similar determinism in human actions. Venn maintained that probability statements (...) were intelligible solely as projections of the ultimate frequency of an outcome in an unlimited series of trials and therefore led to no inferences about free will. An issue here was Venn's claim that although the aggregate probability may be stable, the individual events were completely irregular and, in fact, displayed randomness. Venn's concept of randomness was really apparent, or pseudo-, randomness, which could be totally determined. Ironically, Venn's frequentist position was very useful to the growing field of statistics, which could develop correlations and predictive models empirically without having to address implications for personal freedom or fatalism. (shrink)