401-3628-14L Bayesian Statistics
|Periodizität||2-jährlich wiederkehrende Veranstaltung|
|Kurzbeschreibung||Introduction to the Bayesian approach to statistics: decision theory, prior distributions, hierarchical Bayes models, empirical Bayes, Bayesian tests and model selection, empirical Bayes, Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods.|
|Lernziel||Students understand the conceptual ideas behind Bayesian statistics and are familiar with common techniques used in Bayesian data analysis.|
|Inhalt||Topics that we will discuss are:|
Difference between the frequentist and Bayesian approach (decision theory, principles), priors (conjugate priors, noninformative priors, Jeffreys prior), tests and model selection (Bayes factors, hyper-g priors for regression),hierarchical models and empirical Bayes methods, computational methods (Laplace approximation, Monte Carlo and Markov chain Monte Carlo methods)
|Skript||A script will be available in English.|
|Literatur||Christian Robert, The Bayesian Choice, 2nd edition, Springer 2007.|
A. Gelman et al., Bayesian Data Analysis, 3rd edition, Chapman & Hall (2013).
Additional references will be given in the course.
|Voraussetzungen / Besonderes||Familiarity with basic concepts of frequentist statistics and with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed.|