Syllabus for |
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| MVE187 - Computational methods for Bayesian statistics |
| Beräkningsmetoder för Bayesiansk statistik |
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| Syllabus adopted 2019-02-26 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits
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| Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail |
| Education cycle: Second-cycle |
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Major subject: Mathematics |
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
Application code: 20131
Open for exchange students: Yes
| Module |
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0117 |
Project |
2,0c |
Grading: UG |
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2,0c
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| 0217 |
Examination |
5,5c |
Grading: TH |
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5,5c
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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.