Course syllabus for Computational methods for Bayesian statistics

Course syllabus adopted 2023-02-14 by Head of Programme (or corresponding).

Overview

  • Swedish nameBeräkningsmetoder för Bayesiansk statistik
  • CodeMVE187
  • Credits7.5 Credits
  • OwnerMPENM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 20114
  • Open for exchange studentsYes

Credit distribution

0117 Project 2 c
Grading: UG		2 c0 c0 c0 c0 c0 c
0217 Examination 5.5 c
Grading: TH		5.5 c0 c0 c0 c0 c0 c
  • 28 Okt 2023 am J
  • 29 Aug 2024 am J

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Basic skills in mathematical statistics.
Basic skills in scientific programming (for example in Matlab or R) as achieved by completing TMS150 "Stochastic Data Processing and Simulation".

Aim

In Bayesian statistical analysis and decision theory, calculating exact results is often intractable due to the complexity of the involved models and their parameter spaces. This course aims at equipping the student with practical and theoretical skills for utilizing computationally intensive methods to solve such tasks, in particular in the form of stochastic simulations.

A special effort will be made to help the student to see the connections and interplay between statistical modeling and applied problem solving, as well as computational and theoretical aspects of the models.

Learning outcomes (after completion of the course the student should be able to)

On successful completion of the course the student will be able to
  • explain and apply a Bayesian approach to probability inference,
  • implement important computational algorithms for Bayesian inference, for example Metropolis-Hastings MCMC,
  • make independent and informed decisions about statistical modeling and
    computational choices,
  • present his or her analysis in a structured and pedagogical way.


Content

  • Philosophy of Bayesian statistics.
  • Conjugate priors and improper priors.
  • Approximate methods for low-dimensional parameter spaces.
  • Basic sampling methods.
  • Monte Carlo integration.
  • Advanced sampling methods such as Markov chain Monte Carlo (MCMC).
  • Hierarchical models.
  • Computations for Bayesian Networks.
  • Basic information theory.
  • The EM algorithm.
  • Basic variational Bayes methods.

Organisation

Lectures and obligatory computer based hand-in assignments.

Literature

A compendium written for the course, and in addition, some supporting literature:
  • Excerpts from Albert: Bayesian Computation with R (2009) Springer (ISBN 978-0-387-92297-3). Available in electronic format through the Chalmers library.
  • Excerpts from Bishop: Pattern Recognition And Machine Learning (2006) Springer (ISBN-10: 0-387-31073-8). Available on-line.
  • Excerpts from Robert & Casella: Introducing Monte Carlo Methods with R (2010) Springer (ISBN: 978-1-4419-1575-7). Available in electronic format through the Chalmers library.

Examination including compulsory elements

Compulsory computer based hand-in assignments. The grade will be based on a written examination at the end of the course.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.