Covers the theory of Markov Chain Monte Carlo (MCMC) sampling and discusses convergence conditions, transition matrix choice, and target distribution evolution.
Explores the influence of complexity on ergodic properties of symbolic systems, presenting the Curtis-Hedlund-Lyndon Theorem and constructions of minimal subshifts.
Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.
Introduces Hidden Markov Models, explaining the basic problems and algorithms like Forward-Backward, Viterbi, and Baum-Welch, with a focus on Expectation-Maximization.
Explores Markov chains, Metropolis-Hastings, and simulation for optimization purposes, highlighting the significance of ergodicity in efficient variable simulation.