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Graduate courses

Departments' graduate courses for PhD-students.

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Syllabus for

Academic year
SSY315 - Bayesian statistics  
Bayesiansk statistik
 
Syllabus adopted 2020-03-24 by Head of Programme (or corresponding)
Owner: MPCOM
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: Second-cycle
Major subject: Electrical Engineering
Department: 32 - ELECTRICAL ENGINEERING

The course round is cancelled. For further questions, please contact the director of studies MPCOM: COMMUNICATION ENGINEERING, MSC PROGR, contact information can be found here. This course round is given every other year. Is not given 2019/2020


Teaching language: English
Application code: 13112
Open for exchange students: Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0114 Project 7,5 c Grading: TH   7,5 c    

In programs

MPCOM COMMUNICATION ENGINEERING, MSC PROGR, Year 1 (elective)
MPDSC DATA SCIENCE AND AI, MSC PROGR, Year 1 (elective)

Examiner:

Alexandre Graell i Amat

  Go to Course Homepage


Eligibility:


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Students must have passed SSY130 Applied Signal Processing, or a similar course. This implies working knowledge of basic probability, statistics, and linear algebra. Basic MATLAB programming skills are also required in order to complete the home assignments and the course projects.

Aim

The goal of this course is to provide the students with several important tools to tackle general estimation and detection problems from a rigorous Bayesian perspective. We will describe the philosophy behind Bayesian statistics, the benefits and pitfalls of priors, the inherent computational challenges, and classic and modern inference tools. Through homework problems, students will get hands-on experience with these tools and apply them to a variety of problems.

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

After the course, the students should be able to
  • Explain the philosophy behind Bayesian statistics and its benefits compared to classical frequentist statistics.
  • Develop an inference algorithm (an estimator or a detector) using the principles of Bayesian decision theory and a given cost function.
  • Derive fundamental performance bounds and describe under which conditions they are valid.
  • Select an appropriate prior based on prior knowledge and computational constraints.
  • Design sampling methods and use them to compute integrals such as a posterior mean.
  • Understand, explain, and apply a large set of tools including Laplace approximations and nonparametric models such as Gaussian processes.

Content

We describe the key elements of Bayesian statistics, which is a prominent methodology for making decisions of different types. We cover the following important topics:
  • Bayesian philosophy
  • Likelihood and duality principles
  • Basic decision theory
  • Conjugate, noninformative and hierachical priors
  • Sampling methods
  • Laplace method and Bayesian information criterion
  • Bayesian Cramér-Rao bounds
  • Consensus algorithms for distributed inference
  • Nonparametric Bayesian models.

Organisation

The course comprises
  • lectures
  • weekly home assignments
  • tutorial sessions related to the home assignments.

Literature

We will mainly use Christopher M. Bishop, "Pattern Recognition and Machine Learning", Springer, 2006

Examination including compulsory elements

To pass the course you are required to:

  1. Complete a minimum number (to be communicated on a weekly basis) of the homework assignments;
  2. Grade another group's homework every week; and
  3. Present a research paper at the end of the course, which you may select from a list that we will publish on the website.

There is no written exam.


Page manager Published: Thu 04 Feb 2021.