Course manual 2019/2020
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
- The student knows the definitions of the model distributions, prior distribution, posterior distribution, prior predictive distribution and posterior distribution
- The student is able to calculate the posterior distribution given a statistical model and prior distribution
- The student is able to calculate the following Bayesian point estimators: Maximum-a-posterior estimator and Posterior mean
- The student is able to construct credible sets and HPD-credible sets
- The student is able to calculate the prior odds, posterior odds and Bayes factor given a statistical model and prior distribution
- The student knows the definitions of Loss, Risk and Bayes risk and is able to apply them for statistical decision problems
- The student is able to compare the Bayesian methods for point-estimation, credible sets, hypothesis testing and statistical decision theory to the corresponding methods in frequentist statistics
- The student is able to explain the difference between subjective and objective priors
- The student is able to calculate the Jeffreys prior for a statistical model
- The student is able to determine whether a collection of probability distributions is a conjugate family for a given model
- The student knows the definitions of hyperparameters and hyperpriors and is able to construct the prior for the original parameter given a sequence of hyperpriors and determine the corresponding posterior distribution
- The student is able to calculate the ML-II estimator for a hyperparameter of a prior distribution
- The student is able to do an analysis of the Bayesian methods from a frequentist point of view
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.
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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.
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It is not allowed to miss obligatory parts of the programme's component if there is no case of circumstances beyond one's control.
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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.
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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
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, 1.2, 1.3, 1.4 |
| 2 |
Prior, posterior & model distributions, Bayes's Rule |
Subsection 2.1.1, app B.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 — 2.1.5 |
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 midterm |
| 10 |
Jeffreys prior |
Section 3.3, 3.4.1 |
3.1, 3.2 |
| 11 |
Conjugate priors |
Section 3.4.2, 3.5, 3.6 |
3.3, 3.4 (a, c, e) |
| 12 |
Hyperparameters, hyperpriors, ML-II estimation |
Sections 6.4, app D.1, D.2 |
3.6, 3.7 |
| 13 |
Dirichlet distribution, Dirichlet process prior |
Section 4.1, 4.2 |
4.2, 4.3, 4.5 |
| 14 |
Final exam |
|
|
The schedule for this course is published on DataNose.
There is no honours extension to this course.
Recommended prerequisites: Measure Theory
Processed course evaluations
Below you will find the adjustments in the course design in response to the course evaluations.
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