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.
One very famous statistician has a short PowerPoint presentation at
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.