Topics in Statistics

Knowledge:

• Principles and theory behind the Metropolis-Hastings algorithm and Gibbs sampling
• Key concepts of slice sampling and how it compares to other MCMC methods
• Insights into tempering/annealing for overcoming multimodal posteriors
• Fundamentals of Hamiltonian Monte Carlo, including its advantages in high-dimensional spaces
• Common challenges such as convergence diagnostics and autocorrelation in MCMC simulations
• Applications of MCMC methods to complex inference problems in Bayesian statistics

Skills: Ability to

• Design and implement MCMC algorithms for various statistical models
• Apply Metropolis-Hastings, Gibbs sampling, slice sampling, and Hamiltonian Monte Carlo to practical problems
• Analyze and diagnose convergence issues in MCMC simulations using trace plots and statistical tests
• Compare different MCMC methods in terms of computational efficiency and statistical performance

Competences: Ability to

• Critically assess the suitability of different MCMC algorithms for a given statistical problem
• Evaluate the performance of an MCMC method, including its convergence and mixing properties
• Present complex concepts related to MCMC theory and applications clearly and effectively