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I have been very interested lately in learning Bayesian Statistics, but I have only a little bit of background in the frequentist statistics, only one term at University.

Some of the books that I have seen are extremely mathematically oriented like:

  • Bayesian Theory, José Bernardo. Probability and Statistics, Degroot
    (this is actually a nice book, but it jumps too much between chapters in the examples, making the process of reading pretty sequential in all the book)

The topics that I would like to learn are:

  • Bayesian inference.
  • Generation of independent samples from distributions.
  • Monte Carlo integration, importance sampling.
  • Posterior distribution with numerical quadrature or Laplace expansion.
  • MCMC methods: Gibbs and Metropolis-Hastings sampling.
  • Auxiliary variable methods in MCMC.
  • EM algorithm.
  • Multi-model inference.
  • MCMC theory.

I have tried to find something in Coursera but nothing. What books or online courses do you recommend?

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If you are looking for something introductory, I suggest you to have a look at John Kruschke's "Doing Bayesian Data Analysis". It's fun (believe me!) and not too technical, and will certainly work as an introduction to some of the topics you mentioned.

It is really oriented as a "recipe-book". I mean, you will find some theoretical stuff and fundaments, but not in detail, because this was obviously written for people who need to conduct sound Bayesian data analysis right now.

The book uses R and BUGS, but the scripts are available for JAGS too.

I really recommend it, unless you are looking for more advanced stuff.

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I really like "Data Analysis: A Bayesian Tutorial" by Sivia (the second addition is also co-authored by Skilling). It doesn't go into a huge amount of depth but is very hands on and explains the core concepts and basic implementations very clearly without any fuss.

At the other end of the spectrum is "Probability Theory: The Logic of Science" by Jaynes. This polemic gives you a great explanation of the logic behind the Bayesian approach and a firm theoretical basis without going into too much mathematical detail. It does not however provide much in the way of practical details about implementing algorithms for solving practical problems.

Reading those two books (in either order) provide a nice complementary introduction to Bayesian statistics.

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