“Bayesian Statistics the Fun Way: Understanding Statistics and Probability with Star Wars, Lego, and Rubber Ducks,” by Will Kurt (2019 No Starch Press) is an excellent introduction to subjects ...
Confessions of a moderate Bayesian, part 4 Bayesian statistics by and for non-statisticians Read part 1: How to Get Started with Bayesian Statistics Read part 2: Frequentist Probability vs Bayesian Probability Read part 3: How Bayesian Inference Works in the Context of Science Predictive distributions A predictive distribution is a distribution that we expect for future observations. In other ...
The basis of all bayesian statistics is Bayes' theorem, which is $$ \mathrm {posterior} \propto \mathrm {prior} \times \mathrm {likelihood} $$ In your case, the likelihood is binomial. If the prior and the posterior distribution are in the same family, the prior and posterior are called conjugate distributions.
Which is the best introductory textbook for Bayesian statistics? One book per answer, please.
A Bayesian model is a statistical model made of the pair prior x likelihood = posterior x marginal. Bayes' theorem is somewhat secondary to the concept of a prior.
I'm going to take your questions in order: The question is, Who are the Bayesians today? Anybody who does Bayesian data analysis and self-identifies as "Bayesian". Just like a programmer is someone who programs and self-identifies as a "programmer". A slight difference is that for historical reasons Bayesian has ideological connotations, because of the often heated argument between proponents ...
In a Bayesian framework, we consider parameters to be random variables. The posterior distribution of the parameter is a probability distribution of the parameter given the data. So, it is our belief about how that parameter is distributed, incorporating information from the prior distribution and from the likelihood (calculated from the data).