Math faculty here give one hour talks on topics of interest to our Math 290-Mathematical Perspectives class . I use this opportunity to explore a current interest and organize my thoughts. This year I decided to do an introduction to Bayesian analysis and developed a narrative that moved from the general idea of factoring in prior probabilities in everyday life, to finding a two-headed coin, to Bayesian tables, to visions of simulating changing posterior probabilities and then I gave up. On the most basic level people already know and use Bayesian ideas but it was beyond my capabilities to make probabilities and likelihoods compelling. By the way Jordan Ellenberg’s new book How Not to Be Wrong follows roughly my imagined outline. Anyway I feel confident that such a lecture would work well for some sort of advanced statistics class if followed by a carefully selected homework set but not for beginning students.
I wanted to make a compelling argument for the centrality of Bayesian thinking and its needed application in the field of statistics. Is this possible? Does the understanding of the Bayesian idea involve too much technical background? Is it possible to build a map from human experience to probabilities that is convincing and instinctual? Maybe science has evolved to the point that its connection to experience is just too far removed.