1. komponenta

Lecture type	Total
Lectures	20
Exercises	10

* Load is given in academic hour (1 academic hour = 45 minutes)

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, accept-reject sampling, Markov chain Monte Carlo (MCMC).

1. Sivia, D., Skilling, J. 2001: Data Analysis: A Bayesian Tutorial. Oxford University Press, 246 pp.
2. Gegory, P. 2005: Bayesian Logical Data Analysis for the Physical Sciences. Oxford University Press, 468 pp.
3. Jaynes, E. T. 2003: Probability Theory: The Logic of Science. Cambridge University Press, 727 pp.
4. MacKay, D. 2003: Information Theory, Inference, and Learning Algorithms. Cambridge University Press, 628 pp.
5. Bolstad, W. M. 2007: Introduction to Bayesian Statistics. John Wiley & Sons, 437 pp.
6. Gelman, A., Carlin, J. B., Stern, H. S., Rubin 2004: Bayesian Data Analysis. Chapman & Hall/CRC, 668 pp.

Geofizika - izborni predmeti - Regular study - Geophysics