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Syllabus for

Academic year
MVE187 - Computational methods for Bayesian statistics
Beräkningsmetoder för Bayesiansk statistik
 
Syllabus adopted 2019-02-26 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English
Application code: 20131
Open for exchange students: Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0117 Project 2,0c Grading: UG   2,0c    
0217 Examination 5,5c Grading: TH   5,5c   29 Oct 2020 am J

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 2 (elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)
MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 1 (elective)
MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 2 (elective)

Examiner:

Petter Mostad

  Go to Course Homepage


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 in models of limited complexity
  • 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

  • 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.
  • Some additional lecture notes.

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.


Published: Mon 28 Nov 2016.