Computational Statistics

What it is about

You will learn methods of computational statistics for high-dimensional, hierarchical, and latent data structures and how to apply them. The focus is on simulation (univariate and multivariate), Bayesian inference with MCMC (Gibbs, Metropolis-Hastings, Hamiltonian MC), bootstrap procedures and the EM algorithm for missing or latent data. In the end you can theoretically understand the algorithms, implement them in R, and interpret results statistically.

What you will be able to do

• Generate random variables theoretically
• Understand Bayesian principles and derive posterior distributions
• Construct Bayesian credible intervals
• Know stationarity and limiting distributions of Markov chains
• Construct, implement, and assess convergence of MCMC samplers
• Apply bootstrap to estimate standard errors and confidence intervals
• Apply EM algorithm for missing and latent structures

What the module consists of

• VorlesungIntroduction to concepts, derivations, and illustrations on real datasets
• Übung/TutorialExercise sheets with theoretical and practical tasks for independent deepening; tutors are available for consultation
• SelbststudiumWorking on exercises and implementation in R

Teaching method

• LectureConcepts and theory are derived and illustrated with real-world examples
• Exercise course / TutorialsPractical and theoretical tasks to reinforce and practice independently; possibility to ask tutors questions
• Self-study assignmentsDeepening and implementation of the algorithms between sessions