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How can one easily and quickly grasp the idea of Bayesian statistics and modelling? I can understand the Bayesian theorem on conditional probabilities, I understand how frequentist statistics works (test statistics, p-values, hypothesis testing...), I understand some ideas of Bayesian statistics, but how does Bayesian inference work (technically) - that's still a little mystery to me.

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A lot of introductory lectures on Bayesian inference can be found with Google. As it stands, your question is very broad and is likely to gather a collection of links to such tutorials. What are you interested in: How do the frequentist and bayesian approaches compare each other (e.g., when interpreting a p-value)? When to use one or the other? Please, add any details that might help to refine your question. – chl♦ Aug 18 '11 at 9:15
@chl, thanks. I updated the question. I already understand things like this, but not how it actually works. Thanks, Tomas – Tomas Aug 18 '11 at 9:54

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One very famous statistician has a short PowerPoint presentation at

http://www.stat.ufl.edu/~casella/Talks/BayesRefresher.pdf

explaining the difference between the Bayesian and frequentist approaches. If you need an application to understand what is going on with the Bayesian techniques, an excellent article entitled "Basketball, Beta, and Bayes" written by Matthew Richey and Paul Zorn in Mathematics Magazine, Vol. 78, No. 5 (Dec., 2005), pp. 354-367 can clear up any confusion.

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Thanks for a good presentation, it was (partially) useful :-) – Tomas Aug 23 '11 at 18:47

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