Contents: Bayesian probability theory and Bayesian inference. Bayesian models and their analysis. Computational methods, Markov-chain Monte Carlo.
After the course, the student can explain the central concepts in Bayesian statistics, and name steps of the Bayesian modeling process. The student can recognize usages for common (i.e. those presented during the course) statistical models, and formulate the models in these situations. The student can compare the most popular Bayesian simulation methods, and implement them. The student can use analytic and simulation based methods for learning the parameters of a given model. The student can estimate the fit of a model to data and compare models.
Assessment: Exercises (48 points), a project work (24 points) and an oral presentation (may adjust project work score). Minimum of 50% of points must be obtained from both the exercises and project work. See more in Assignments and project work.
Self-study is possible: Lectures are not mandatory. Exercise sessions are not mandatory. Mandatory exercises are handed-in online. Mandatory oral presentation needs to be given in the end of the course.
Prerequisites: Differential and integral calculus, basics of probability and statistics, basics of programming (R or Python). Recommended: matrix algebra.
- Basic terms of probability theory
- probability, probability density, distribution
- sum, product rule, and Bayes' rule
- expectation, mean, variance, median
- in Finnish, see e.g. http://math.aalto.fi/~lleskela/LectureNotes003.html
- in English, see e.g. Wikipedia and https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/
- Basic visualisation techniques (R or Python)
Course contents following BDA3. See more in Materials.
- Background (Ch 1)
- Single-parameter models (Ch 2)
- Multiparameter models (Ch 3)
- Computational methods (Ch 10)
- Markov chain Monte Carlo (Ch 11--12)
- extra material for Stan and probabilistic programming
- Hierarchical models (Ch 5)
- Model checking (Ch 6)
- Evaluating and comparing models (Ch 7) + extra material
- Decision analysis (Ch 9)
- Large sample properties and Laplace approximation (Ch 4)
- In addition you learn workflow for Bayesian data analysis