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402-0738-10L 4 Credits DR , MSC D-PHYS
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Bayesian Statistical Methods and Data Analysis

Lecturers & Examiners: Dr. Tilman Tröster
Block course
VVZ CR n/a

Last Updated: 2026-02-05 16:22:41

Abstract

This course covers various data analysis methods using Bayesian statistics, with a focus on practical problem solving. We will discuss Bayesian reasoning, the role of priors, model comparisons, and computational tools for Bayesian statistical inference. We will analyse temporal and spatial data inspired by real astrophysical analyses, using both classical statistical methods and machine learning.

Objective

The goal of this course is to introduce students to Bayesian statistics and prepare them to solve statistical inference problems in contemporary (astrophysics) research. After introducing Bayesian statistics and general methodology, the course will focus on methods to analyse temporal and spatial data such as those encountered in astrophysics. The methods are general and applicable beyond (astro)physics, however.

Content

Topics covered include: Review of probability theory: - Independence, joint and conditional probabilities - Univariate and multivariate probability distributions - Change of variables Bayesian statistics: - Bayes’ theorem - Priors - Bayesian reasoning, model comparison Tools for statistical inference: - Markov chain Monte Carlo (Metropolis Hastings, slice sampling) - Nested sampling, variational inference Analysis of temporal and spatial data: - Summary statistics: covariance, power spectrum - Gaussian processes and Gaussian random fields - Examples from astrophysics The lectures are accompanied with code examples, both to illustrate the covered topics and to demonstrate how the theoretical concepts can be implemented in practical computational inference problems. The students complete a project on a statistical analysis, using the tools covered in the course.

General Information

Language
English
Levels
DR , MSC

Examination

Type
graded semester performance

Registration & Places

Max Places
35

Course Components

Type Title Time & Place Hours
lecture Bayesian Statistical Methods and Data Analysis
Block course
  • 12.06. - 16.06 Date 14:45-16:30 (HIT H 42)
  • 19.06. - 23.06 Date 14:45-16:30 (HIT F 11.1)
20 h semesterly
exercise Bayesian Statistical Methods and Data Analysis
Block course
  • 12.06. - 16.06 Date 16:45-17:30 (HIT H 42)
  • 19.06. - 23.06 Date 16:45-17:30 (HIT F 11.1)
10 h semesterly

Offered In