Bayesian statistics
Summary
A first introduction to Bayesian statistics, assuming knowledge from first courses in statistics and probability. We will focus on foundational statistical and mathematical aspects such as the decision theoretic background, consistency for large sample sizes, and algorithms for Bayesian computation.
Content
Probabilistic foundations and the Bayesian paradigm
- Bayes's formula
- Bayesian estimation, testing and credible regions
Decision-theoretic foundations
- Minimax and Bayes methods, admissibility
- Complete class theorem
Conjugate models
Frequentist analysis of Bayesian methods
- Consistency of Bayesian methods
- Bernstein-von Mises theorem
Bayesian computation via Monte Carlo methods
- Introduction to Markov Chains
- Markov Chain Monte Carlo (MCMC) algorithms
Relevant literature:
- Aad van der Vaart, Botond Szabo: Bayesian Statistics
- Christian Robert: The Bayesian Choice (2007)
- Peter Hoff: A First Course in Bayesian Statistical Methods (2009)
Keywords
Bayes' theorem
Decision theory
Minimax estimation theory
Bernstein-von Mises theorem
Markov Chain Monte Carlo (MCMC)
Bayesian computation
Learning Prerequisites
Required courses
Introductory courses in statistics and probability are necessary. Knowledge of measure-theoretic probability is beneficial.
Assessment methods
Written exam
In the programs
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Bayesian statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Bayesian statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Spring
- Exam form: Written (summer session)
- Subject examined: Bayesian statistics
- Courses: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
Reference week
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Légendes:
Lecture
Exercise, TP
Project, Lab, other