Teaching plan for the course unit

 General information

Course unit name: Bayesian Statistics and Probabilistic Programming

Course unit code: 572663

Coordinator: Jose Fortiana Gregori

Department: Department of Mathematics and Computer Science

Credits: 6

Single program: S

 Estimated learning time Total number of hours 150

 Face-to-face learning activities 60
 -  Lecture with practical component 60
 Supervised project 30
 Independent learning 60

 Recommendations

 Students are assumed to have the basic background in elementary probability and statistics included in curricula qualifying for admission to this master’s degree.

 Competences to be gained during study

 CE5 -     To know how to hypothesize and develop the intuition about a data set using exploratory analysis techniques. CE7 -     To understand, develop and modify analytic and exploratory algorithms operating on data, being these tasks guided by a critical thought. CE8 -  To be able to assess the validity of hypotheses by means of data analytics.

 Learning objectives
 Referring to knowledge To master the Bayesian paradigm as the framework where assumptions and experimental evidences are quantitatively blended into a new outlook.      To apply Bayesian thought to data modeling and prediction.   To understand the rationale of and to know how to bring into practice Bayesian computations, mainly based on simulation.   To be informed about and to be able to use ad hoc computer languages, specifically designed with the aim to handling probability distributions and their simulation.

 Teaching blocks

1. Probability

2. Random variables

3. Simulation

5. Markov chains

6. Bayesian binomial model

7. More conjugate models

8. Monte-Carlo methods

9. Prior distributions

10. MCMC with a continuous state space

11. Gibbs sampling

12. Programming Bayesian simulations

13. MCMC convergence diagnostics.

14. Hamiltonian Monte Carlo

15. Bayesian linear and generalized linear models.

 Teaching methods and general organization

 Sessions will combine pieces of theoretical exposition with application problems and hands-on computer experiments, avoiding separated "formal lectures" or "laboratory sessions". When appropriate, students organized in small groups will deal with problem solving or discussion subjects.

 Official assessment of learning outcomes

 Class participation, including written/coding assignments, will be worth 30% of the final grade. A course project will be worth 30% of the final grade. A written examination (including programming activities) will be worth 40% of the final grade.      Examination-based assessment A course project will be worth 30% of the final grade. A written examination (including programming activities) will be worth 70% of the final grade.