In this updated episode we give plausible expression to a fundamental relationship we will discover between observed data and unobserved hypotheses. The relationship allows us to invert conditional probabilities. The Reverend Thomas Bayes (1763) discovered this rule based on a suggestion by Abraham de Moivre (1756) in his Doctrine of Chances. in It was all but abandoned to a frequentist approach popularized and systematized by Ronald A. Fisher (1928). The Bayesian approach is (probably!) better named a probabilistic approach to inference. In most textbooks there is often a very slender chapter devoted to Bayesian calculations and usage. We invert this tendency in this course. There is only a short reference to the relatively less principled frequentist approach learned as the mainstay in nearly all basic statistics course. There, you just had the short, and nearly the only reference, to a frequentist approach. Absolutely no calculus is required here, just the ability to count up to 17, work with rational integers, all with the algebraic knowledge that any integer divided by itself is the integer 1 and that any integer or algebraic expression for that matter times 1 is just itself.
References
Bayes, T. (1763). LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, FRS communicated by Mr. Price, in a letter to John Canton, AMFR S. Philosophical transactions of the Royal Society of London, (53), 370-418.
De Moivre, A. (1756). The doctrine of chances: A method of calculating the probabilities of events in play. Routledge.
Fisher, R. A. (1928). Statistical methods for research workers (No. 5). Oliver and Boyd.
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