Bayesian Statistics (BSc)

6 EC

Semester 2, period 4, 5

5122BAST6Y

Owner Bachelor Wiskunde
Coordinator dr. B.J.K. Kleijn
Part of Exchange Programme Faculty of Science, specialisation BSc Mathematics, year 1Bachelor Wiskunde, year 3Dubbele bachelor Wiskunde en Informatica, year 3

Course manual 2018/2019

Course content

In frequentist statistics we assume that the data is distributed according to some unknown probability distribution. In Bayesian statistics, the data and the parameter are both treated as a random variable. Besides specifying the statistical model, the Bayesian procedure also specifies a prior distribution on the model. The data will be used as an updating mechanism for the prior resulting in the posterior distribution.

In this course we consider the consider the classical problems considering point-estimation, hypothesis testing, confidence sets and decision theory where we will describe the Bayesian and frequentist methods and compare them to each other. Furthermore, we will discuss the choice of the prior distribution, depending on both the statistical model and the intended posterior distribution.

Study materials

Syllabus

Objectives

  • Begrip van de basiseigenschappen van Bayesiaanse statistische methoden, naast en in vergelijking met frequentistische statistiek.
  • Begrip van de reikwijdte en beperkingen van Bayesiaanse methoden, zowel in praktisch-heuristische als in wiskundig-technische zin.

Teaching methods

    • Lectures 
    • Exercise classes

    Learning activities

    Activiteit

    Aantal uur
    Lectures

    26

    Exercise classes

    26 

    Mid-term exam

    3

    Final exam

    3

    Zelfstudie

    110

    Attendance

    Programme's requirements concerning attendance (OER-B):

    • Each student is expected to actively participate in the course for which he/she is registered.
    • If a student can not be present due to personal circumstances with a compulsory part of the programme, he / she must report this as quickly as possible in writing to the relevant lecturer and study advisor.
    • It is not allowed to miss obligatory parts of the programme's component if there is no case of circumstances beyond one's control.
    • In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are stated in advance in the course manual and on Canvas.
    • In the first and second year, a student should be present in at least 80% of the seminars and tutor groups. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, the student is expelled from the resit of this course. In case of personal circumstances, as described in OER-A Article A-6.4, an other arrangement will be proposed in consultation with the study advisor.

    Assessment

    Item and weight Details

    Final grade

    0.3 (30%)

    Mid-term exam

    0.7 (70%)

    Final exam

    In case of a resit, the resit will completely replace the final grade.

    Inspection of assessed work

    Contact the course coordinator to make an appointment for inspection.

    Fraud and plagiarism

    The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

    Course structure

    Weeknummer Onderwerpen Studiestof Exercises
    1 Frequentist statistics, introduction Bayesian statistics  Sections 1.1, 1.2, 1.3  1.1, 1.5, 1.2
    2 Prior, posterior & model distributions, Bayes's Rule  Subsection 2.1.1, appendix A.5  2.2, 2.3, 2.4
    3 Bayes's billiard, Bayesian view of the model, frequentist view of the posterior  Subsections 2.1.2 — 2.1.4 2.1, 2.5
    4 Bayesian point estimators  Section 2.2 2.7, 2.9, 2.10, 2.11
    5 Confidence sets and credible sets  Section 2.3  2.14, 2.15, 2.13
    6 Tests and Bayes factors  Section 2.4  2.16, 2.17
    7 Decision theory  Section 2.5  2.18, 2.19
    8 Mid-term exam    
    9 Subjective priors, non-informative priors Sections 3.1, 3.2  Discuss mid-term exam
    10 Jeffreys prior  Section 3.2  3.1, 3.2
    11 Conjugate priors  Section 3.3 3.3, 3.4ace
    12 Hyperparameters, hyperpriors, ML-II estimation  Sections 3.4, 3.5 3.6, 3.7
    13 Dirichlet distribution, Dirichlet process prior Section 3.6 Extra material
    14 Final exam     

    Timetable

    The schedule for this course is published on DataNose.

    Honours information

    There is no honours extension to this course.

    Additional information

    Recommended prerequisites: Measure Theory

    Processed course evaluations

    Below you will find the adjustments in the course design in response to the course evaluations.

    Contact information

    Coordinator

    • dr. B.J.K. Kleijn

    Staff

    • Mike Derksen