Basics: deductive vs. inductive reasoning, Cox axioms and probability, Bayes theorem, some history. Parameter estimation: elementary examples, short description of the posterior, the role of prior, generalization to two and more dimensions, relationship with methods of maximal likelihood and least squares. Model comparison: evidence for the model, Bayes factor, Ocam's rule. Assigning probabilities: the indifference principle, groups of transformations, parameters of location and scale, maximum entropy principle. Monte Carlo methods for sampling from posterior: uniform sampling, importance sampling, acceptreject sampling, Markov chain Monte Carlo (MCMC).

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