Bayesian Statistics

Study Course Description

Course Description Statuss:Approved

Course Description Version:3.00

Study Course Accepted:15.03.2024 09:16:16

Study Course Information
Course Code:		SL_111		LQF level:		Level 7
Credit Points:		2.00		ECTS:		3.00
Branch of Science:		Mathematics; Theory of Probability and Mathematical Statistics		Target Audience:		Life Science
Study Course Supervisor
Course Supervisor:		Ziad Taib
Study Course Implementer
Structural Unit:		Statistics Unit
The Head of Structural Unit:
Contacts:		23 Kapselu street, 2nd floor, Riga, statistikarsu[pnkts]lv, +371 67060897
Study Course Planning
Full-Time - Semester No.1
Lectures (count)		10	Lecture Length (academic hours)		2	Total Contact Hours of Lectures		20
Classes (count)		3	Class Length (academic hours)		3	Total Contact Hours of Classes		9
Total Contact Hours								29
Part-Time - Semester No.1
Lectures (count)		10	Lecture Length (academic hours)		1	Total Contact Hours of Lectures		10
Classes (count)		3	Class Length (academic hours)		2	Total Contact Hours of Classes		6
Total Contact Hours								16
Study course description
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.
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.
Topic Layout (Full-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Basics concepts. Likelihood. Bayesian inference. The Bernoulli model. (Ch. 1, 2.1-2.5)			Lectures		1.00	auditorium
2	The Normal model. The Poisson model. Conjugate priors. Prior elicitation. Jeffrey’s prior. (Ch. 2.6-2.9)			Lectures		1.00	auditorium
3	Bayesian inference in R for Bernoulli and normal data. Credibility intervals. The Bolstad R package. (Handouts)			Lectures		1.00	auditorium
4	Multi-parameter models. Marginalization. Multinomial model. Multivariate normal model. Ch. 3.			Lectures		1.00	auditorium
5	Computer lab 1: Exploring posterior distributions in one-parameter models by simulation and direct numerical evaluation			Classes		1.00	computer room
6	Prediction. Making Decisions. Estimation as decision. (Ch. 9.1-9.2.)			Lectures		1.00	auditorium
7	Linear Regression. Nonlinear regression. Regularization priors. (Ch. 14 and Ch. 20.1-20.2)			Lectures		1.00	auditorium
8	Classification. Posterior approximation. Logistic regression. Naive Bayes. (Ch. 16.1-16.3)			Lectures		1.00	auditorium
9	Computer lab 2: Polynomial regression and classification with logistic regression			Classes		1.00	computer room
10	Bayesian computations. Monte Carlo simulation. Gibbs sampling. Data augmentation. (Ch. 10-11)			Lectures		1.00	auditorium
11	MCMC and Metropolis-Hastings (Ch. 11)			Lectures		1.00	auditorium
12	Computer lab 3: Applications of MCMC in Bayesian statistics			Classes		1.00	computer room
13	Bayesian model comparison and hypothesis testing. (Ch. 7)			Lectures		1.00	auditorium
Topic Layout (Part-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Basics concepts. Likelihood. Bayesian inference. The Bernoulli model. (Ch. 1, 2.1-2.5)			Lectures		1.00	auditorium
2	The Normal model. The Poisson model. Conjugate priors. Prior elicitation. Jeffrey’s prior. (Ch. 2.6-2.9)			Lectures		1.00	auditorium
3	Bayesian inference in R for Bernoulli and normal data. Credibility intervals. The Bolstad R package. (Handouts)			Lectures		1.00	auditorium
4	Multi-parameter models. Marginalization. Multinomial model. Multivariate normal model. Ch. 3.			Lectures		1.00	auditorium
5	Computer lab 1: Exploring posterior distributions in one-parameter models by simulation and direct numerical evaluation			Classes		1.00	computer room
6	Prediction. Making Decisions. Estimation as decision. (Ch. 9.1-9.2.)			Lectures		1.00	auditorium
7	Linear Regression. Nonlinear regression. Regularization priors. (Ch. 14 and Ch. 20.1-20.2)			Lectures		1.00	auditorium
8	Classification. Posterior approximation. Logistic regression. Naive Bayes. (Ch. 16.1-16.3)			Lectures		1.00	auditorium
9	Computer lab 2: Polynomial regression and classification with logistic regression			Classes		1.00	computer room
10	Bayesian computations. Monte Carlo simulation. Gibbs sampling. Data augmentation. (Ch. 10-11)			Lectures		1.00	auditorium
11	MCMC and Metropolis-Hastings (Ch. 11)			Lectures		1.00	auditorium
12	Computer lab 3: Applications of MCMC in Bayesian statistics			Classes		1.00	computer room
13	Bayesian model comparison and hypothesis testing. (Ch. 7)			Lectures		1.00	auditorium
Assessment
Unaided 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.
Assessment Criteria:
• Active participation in lectures and computer labs – 20%. • Handing out reports on 3 computer labs – 40%. • Final written examination – 40%
Final Examination (Full-Time):		Exam (Written)
Final Examination (Part-Time):		Exam (Written)
Learning Outcomes
Knowledge:		• 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:		• 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.
Competencies:		• 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.
Bibliography
No.	Reference
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.