I followed the link from commenter Lemmus and encountered this list of resources on Bayesian reasoning. These were all fine, but they didn’t look like the Bayesian statistics that I am familiar with. (For example, the wikipedia link defines “A Bayes estimator is a statistical estimator that minimizes the average risk.” Which doesn’t have anything to do with anything that I do!) And the examples are all discrete–which makes sense, that’s a good way to start–but I think it gives a misleading perspective of Bayesian data analysis as a statistical method.

So I thought I’d post Chapter 1 from Bayesian Data Analysis so people could see a practicing statistician’s perspective. (Here’s the table of contents and front matter of the book, to place it in context.)

“Bayesian reasoning” and “Bayesian data analysis” have (almost) the same name, but they’re different things.

P.S. The distinction arises in other fields too. For example, a book on “thinking like a lawyer” will be different than a book on the practice of law, a book on “the engineering way of life” might not be very descriptive of what engineers actually do, and so forth.

P.P.S. If you’re coming from statistics or econometrics, and you want to see how Bayesian inference generalizes classical least squares and maximum likelihood, then Chapter 18 from my book with Jennifer may be the best place to start.