Monte Carlo Methods and Bayesian Statistics

Level of Study

Master

Teaching semester

Spring/Irregular. The course does not run spring 2023.

Objectives and Content

The course provides an introduction to theory and practice in Monte Carlo statistical methods and Bayesian statistics. It aims to provide a good foundation in both fields. Topics covered are the generation of random numbers from different probability distributions, estimation of density functions, Monte Carlo integration, Monte Carlo methods of statistical inference, and the bootstrap. The corse will also provide an introduction to Markov Chain Monte Carlo and Bayesian statistics.

Learning Outcomes

After completing the course, students should be able to:

• Generate of random numbers from (different) probability distributions
• Use/ apply the acceptance-rejection algorithm
• Perform Monte Carlo integration with error evaluation and carry out importance sampling in an integration context
• know acceleration methods such as the use of antithetical variables and control variables
• Use Monte Carlo methods of estimation of density functions and carry out hypothesis tests
• Know the Bootstrap method
• Understand and be able to apply Markov Chain Mojte Carlo (MCMC) including Metropolis-Hastings algorithm and Gibbs sampling
• Understand the Bayesian theorem and can carry out Bayesian inference both theoretically and numerically with MCMC
• Know the concept of Bayesian conjugate prior distributions
• Use Bayesian model selection and Bayesian networks

Required Previous Knowledge

None

Recommended Previous Knowledge

STAT110, STAT111, STAT210 (can be an advantage).

Credit Reduction due to Course Overlap

None

Access to the Course

Access to the course requires admission to a program of study at The Faculty of Mathematics and Natural Sciences

Teaching and learning methods

Lectures / approx. 4 hours pr. week

Computer lab / appro. 2 hours a week for 6 weeks

Compulsory Assignments and Attendance

To mandatory exercises

Forms of Assessment

Oral examination

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.