Statistical Rethinking (2022 Edition)
This is a great book.<p>However, I really hate the "Golem of Prague" introduction. It presents an oversimplified caricature of modern frequentist methods, and is therefore rather misleading about the benefits of Bayesian modeling. Moreover, most practicing statisticians don't really view these points of view as incompatible. Compare to the treatment in Gelman et al.'s Bayesian Data Analysis. There are p-values all over the place.<p>Most importantly, this critique fails on basic philosophical grounds. Suppose you give me a statistical problem, and I produce a Bayesian solution that, upon further examination with simulations, gives the wrong answer 90% of time on identical problems. If you think there's something wrong with that, then congratulations, you're a "frequentist," or at least believe there's some important insight about statistics that's not captured by doing everything in a rote Bayesian way. (And if you don't think there's something wrong with that, I'd love to hear why.)<p>Also, this isn't a purely academic thought experiment. There are real examples of Bayesian estimators, for concrete and practical problems such as clustering, that give the wrong estimates for parameters with high probability (even as the sample size grows arbitrarily large).