Abstract

Lecture: Monday 10 July 2023, 11:15 – 12:15Title: Introduction to stochastic modeling and MCMC methodsPresenter: Christian SOIZE 1. Introduction to stochastic modeling in Uncertainty Quantification (UQ). Aleatory and epistemic uncertainties. Sources of uncertainties and variabilities. Major challenges for the computational models. Brief summary of a strategy in UQ. 2. Multivariate Kernel Density Estimation (KDE) method in nonparametric statistics. Problem definition. Multivariate kernel density estimation method. 3. MCMC methods for generating realizations/samples. Main algorithms for the MCMC method: Metropolis-Hastings, Gibbs sampler,   Langevin Metropolis-Hastings, MCMC Hamiltonian dynamics algorithms. Metropolis-Hastings algorithm. Example and analysis for the Metropolis-Hastings algorithm. MCMC dissipative Hamiltonian dynamics algorithm.- Example and analysis of the ISDE -based algorithm.