Lectures related to Markov Chain Monte Carlo

Covers the concept of geometric ergodicity in the context of convergence diagnostics for Markov chains.

Covers Markov chains, focusing on reversibility, convergence, ergodicity, and applications.

Covers the theory and applications of Markov chains, focusing on key concepts and properties.

Explores the composition of applications in mathematics and the importance of understanding their properties.

Covers stochastic simulation and variance reduction techniques, focusing on Courra variate and auxiliary distribution generation.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Covers the estimation of relaxation time in chains and the importance of sample sizes.

Covers topics in probability theory, focusing on uniform integrability and convergence theorems.

Covers error estimation in Latin Hypercube Sampling, emphasizing the importance of accurate variance estimation.

Explores stratified sampling, dividing a population into subgroups for more accurate sampling.

Covers the Theoreus Chain Role for Lipschitz functions and its practical applications.

Covers weak derivatives, their properties, and applications in functional analysis.

Covers conditional expectation, Fubini's theorem, and their applications in probability theory.

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Covers the concept of outer measure and properties of measurable sets.

Introduces Cartesian product and induction for proofs using integers and sets.

Explores optimal transport in heat equations and metric spaces.

Covers applied probability, stochastic processes, Markov chains, rejection sampling, and Bayesian inference methods.

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.