Statistical Rethinking A Bayesian Course with Examples in R and Stan2

The rise of probability theory changed that. Statistical inference compels us instead to rely on Fortuna as a servant of Minerva, to use chance and uncertainty to discover reliable knowledge. All flavors of statistical inference have this motivation. But Bayesian data analysis embraces it most fully, by using the language of chance to describe the plausibility of different possibilities. There are many ways to use the term “Bayesian.” But mainly it denotes a particular interpretation of probability. In modest terms, Bayesian inference is no more than counting the numbers of ways things can happen, according to our assumptions. Things that can happen more ways are more plausible. And since probability theory is just a calculus for counting, this means that we can use probability theory as a general way to represent plausibility, whether in reference to countable events in the world or rather theoretical constructs like parameters. Once you accept this gambit, the rest follows logically. Once we have defined our assumptions, Bayesian inference forces a purely logical way of processing that information to produce inference.