STAT3190 Bayesian Statistics (5 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Description
Interpretations of Probability. Probabilities as pricing system, De Finetti dutch book argument. Conditional probabilities and Bayes formula. Probability as information and the Bayesian paradigm. The Cox axioms of conditional probability. The likelihood principle. Exponential families of distributions and Conjugate priors. Maximum entropy distributions. Bayesian computational Statistics: Monte Carlo methods, importance sampling and rejection sampling. Markov Chain Monte Carlo. Missing Data and Data augmentation. Bayesian decision theory, Model Choice and Bayes Factors-
Learning outcomes
What you should know after you have completed the course:
Understanding the different interpretations of probability. Applying Bayes formula analytically and also computationally, using the modern computational tools to approximate the posterior distribution, and the software packages written in Julia and/or R.
Description of prerequisites
Probability and Statistics