Veidlapa Nr. M-3 (8)
Study Course Description
Bayesian Statistics
Course Code
SL_111
Branch of Science
Mathematics; Theory of probability and mathematical statistics
ECTS
3.00
Target Audience
Life Science
LQF
Level 7
Study Type And Form
Full-Time; Part-Time
Study Course Implementer
Course Supervisor
Ziad Taib
Structure Unit Manager
Andrejs Ivanovs
Structural Unit
Statistics Unit
Contacts
23 Kapselu street, 2nd floor, Riga, statistika@rsu.lv, +371 67060897
About Study Course
Objective
The objective of this course is to give the students an overview of key areas of Bayesian Inference. The software package R will be used for computation and case study applications.
Preliminary Knowledge
• Familiarity with most common discrete and continuous distributions as well as basic notions of probability.
• Familiarity with basics of statistical inference and Maximum likelihood estimation (MLE).
• Linear models with different types of dependent variables.
• In lab sessions we will learn how to use R, so basic knowledge in R is also required.
Learning Outcomes
Knowledge
1.• Understand the difference between various interpretations of probability. • Classify and articulate the key components of Bayesian Inference. • Distinguish the key aspects, and applications, of prior distribution selection and associated considerations. • Describe the role of the posterior distribution, the likelihood function and the posterior distribution in Bayesian inference about a parameter. • Interpret statistical simulation-based computational methods.
Skills
1.• Formulate Bayesian solutions to real-data problems, including forming hypotheses, collecting and analysing data, and reaching appropriate conclusions. • Calculate posterior probabilities using Bayes’ theorem. • Derive posterior distributions for a given data model and use computational techniques to obtain relevant estimates. • Operate Bayesian models and provide the technical specifications for such models. • Apply Bayesian computation using Markov chain Monte Carlo methods using R.
Competences
1.• Assess the Bayesian framework for data analysis and when it can be beneficial, including its flexibility in contrast to the frequentist approach. • Use independently statistical analyses in practice by using simulation-based computational methods, to present the results and findings orally and in writing. • Determine the role of the prior distribution in Bayesian inference, and the usage of non-informative priors and conjugate priors. • Interpret the results of a Bayesian analysis and perform Bayesian model evaluation and assessment.
Assessment
Individual work
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Individual work |
-
|
-
|
|
1. Individual work with the course material in preparation to all lectures according to plan.
2. Three computer labs according to plan – individual work in pairs on agreed computer assignments. Students will independently analyse data to reach requirements of defined tasks Bayesian methods presented throughout the course and discuss obtained results during computer labs.
|
||
Examination
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Examination |
-
|
-
|
|
• Active participation in lectures and computer labs – 20%.
• Handing out reports on 3 computer labs – 40%.
• Final written examination – 40%
|
||
Study Course Theme Plan
FULL-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Basics concepts. Likelihood. Bayesian inference. The Bernoulli model.
(Ch. 1, 2.1-2.5)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
The Normal model. The Poisson model. Conjugate priors. Prior elicitation. Jeffrey’s prior.
(Ch. 2.6-2.9)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Bayesian inference in R for Bernoulli and normal data. Credibility intervals. The Bolstad R package.
(Handouts)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Multi-parameter models. Marginalization. Multinomial model. Multivariate normal model.
Ch. 3.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
3
|
Topics
|
Computer lab 1: Exploring posterior distributions in one-parameter models by simulation and direct numerical evaluation
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Prediction. Making Decisions. Estimation as decision.
(Ch. 9.1-9.2.)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Linear Regression. Nonlinear regression. Regularization priors.
(Ch. 14 and Ch. 20.1-20.2)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Classification. Posterior approximation. Logistic regression. Naive Bayes.
(Ch. 16.1-16.3)
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
3
|
Topics
|
Computer lab 2: Polynomial regression and classification with logistic regression
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Bayesian computations. Monte Carlo simulation. Gibbs sampling. Data augmentation.
(Ch. 10-11)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
MCMC and Metropolis-Hastings
(Ch. 11)
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
3
|
Topics
|
Computer lab 3: Applications of MCMC in Bayesian statistics
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Bayesian model comparison and hypothesis testing.
(Ch. 7)
|
Total ECTS (Creditpoints):
3.00
Contact hours:
29 Academic Hours
Final Examination:
Exam (Written)
PART-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Basics concepts. Likelihood. Bayesian inference. The Bernoulli model.
(Ch. 1, 2.1-2.5)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
The Normal model. The Poisson model. Conjugate priors. Prior elicitation. Jeffrey’s prior.
(Ch. 2.6-2.9)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Bayesian inference in R for Bernoulli and normal data. Credibility intervals. The Bolstad R package.
(Handouts)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Multi-parameter models. Marginalization. Multinomial model. Multivariate normal model.
Ch. 3.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Computer lab 1: Exploring posterior distributions in one-parameter models by simulation and direct numerical evaluation
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Prediction. Making Decisions. Estimation as decision.
(Ch. 9.1-9.2.)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Linear Regression. Nonlinear regression. Regularization priors.
(Ch. 14 and Ch. 20.1-20.2)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Classification. Posterior approximation. Logistic regression. Naive Bayes.
(Ch. 16.1-16.3)
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Computer lab 2: Polynomial regression and classification with logistic regression
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Bayesian computations. Monte Carlo simulation. Gibbs sampling. Data augmentation.
(Ch. 10-11)
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
MCMC and Metropolis-Hastings
(Ch. 11)
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Computer lab 3: Applications of MCMC in Bayesian statistics
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Bayesian model comparison and hypothesis testing.
(Ch. 7)
|
Total ECTS (Creditpoints):
3.00
Contact hours:
16 Academic Hours
Final Examination:
Exam (Written)
Bibliography
Required Reading
1.
Gelman, A., Carlin, J.B, Stern, H.S and Rubin, D.B. Bayesian Data Analysis 2nd ed. Chapman and Hall, 2003.
Additional Reading
1.
Bolstad, W. M. and Curran, J. M. Introduction to Bayesian Statistics. John Wiley & Sons, Incorporated, 2016.
2.
Hoff, P. D. A First Course in Bayesian Statistical Methods. Springer, 2009.
3.
Kruschke, J. Doing Bayesian Data Analysis. Academic Press, 2015.
4.
Marin, J.-M. and Robert, C.P. Bayesian Essentials with R. New York: Springer, 2013.