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Bayesian Learning

2018VT

Status Open for interest registrations
School Computer and Information Science (CIS)
Division STIMA
Owner Mattias Villani
Homepage https://www.ida.liu.se/~732A91/info/courseinfo.en.shtml

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Course plan

No of lectures

12*2 lecture hours + 4*4 computer lab hours + 4*2 problem solving classes

Recommended for

PhD students in Statistics, Computer Science, and the Engineering Sciences.

The course was last given

Spring 2017

Goals

The course gives a solid introduction to Bayesian learning, with special emphasis on theory, models and methods used in machine learning applications. The student will learn about the basic ideas and concepts in Bayesian analysis from detailed analysis of simple probability models. The course presents simulation algorithms typically used in practical Bayesian work, and course participants will learn how to apply those algorithms to analyze complex machine learning models.
After completing the course the student should be able to:
• derive the posterior distribution for a number of basic probability models
• use simulation algorithms to perform a Bayesian analysis of more complex models
• perform Bayesian prediction and decision making
• perform Bayesian model inference.

Prerequisites

Students admitted to the Master’s programme in Statistics and Data Mining fulfill the admission requirements for the course.
Students not admitted to the Masters’ programme in Statistics and Data Mining should have passed:
an intermediate course in probability and statistical inference
a basic course in mathematical analysis
a basic course in linear algebra
a basic course in programming
It also required to have a basic knowledge of linear regression, either as a part of a statistics course, or as a separate course.

Organization

The course consists of lectures, computer labs and problem solving sessions. The lectures are devoted to presentations of concepts and methods. The computer labs are used for practical applications of Bayesian inference. The problem solving sessions are for applying the theory to concrete problems.
Language of instruction: English.

Contents

Likelihood, Subjective probability, Bayes theorem, Prior and posterior distribution, Bayesian analysis of the following models: Bernoulli, Normal, Multinomial, Multivariate normal, Linear and nonlinear regression, Binary regression, Mixture models; Regularization priors, Classification, Naïve Bayes, Marginalization, Posterior approximation, Prediction, Decision theory, Markov Chain Monte Carlo, Gibbs sampling, Bayesian variable selection, Model selection, Model averaging.

Literature

Bayesian Data Analysis, 3rd edition.

Lecturers

Mattias Villani/Matias Quiroz

Examiner

Mattias Villani

Examination

The course is examined by written reports on computer lab assignments and by a computer exam.

Credit

6 ECTS credits.

Comments

The course is also given within the master programme Statistics and Data Mining, and on the master's level in some engineering programmes.


Page responsible: Director of Graduate Studies
Last updated: 2012-05-03