Il Prof. A. Smith dell'universita' di Ottawa terra' tre lezioni nell'ambito del dottorato in matematica presso il Dip. di Matematica e Fisica di Roma Tre con il seguente programma:
*MIXING OF MARKOV CHAINS ON MANIFOLDS*
Martedi 6 Dicembre ore 11:00-13:00 aula 311
*Mixing Properties of Hamiltonian Monte Carlo*
Abstract:* Hamiltonian Monte Carlo (HMC) and its variants are extremely popular Markov chain Monte Carlo algorithms in statistical computing. In practice, they seem to outperform classical algorithms such as the Gibbs sampler and the Metropolis-Hastings algorithm. Unfortunately, the characteristic long moves made by HMC also make it difficult to analyze. I will survey some existing results on HMC and competitor algorithms, including some recent results of myself and Mangoubi, and present open problems.*
Mercoledi 7 Dicembre ore 14:30-16:30 aula 311
*Convex Sets, Conductance and Curvature.*
Abstract: Geometric random walks are popular tools for sampling from the interior or boundary of convex sets. I will introduce some popular geometric random walks and describe the mathematical techniques developed by Dieker, Kannan, Lovasz, Vempala and others to analyze them. I will then describe how some recent work takes advantage of ideas from geometry and convex optimization to propose and analyze algorithms that can have improved performance.
Martedi 13 Dicembre ore 11:00-13:00 aula 311
*Kac's Walks and Couplings.*
Abstract: Kac's walks on the sphere and on the special orthogonal group. introduced in 1953 and 1970, have long histories in the statistical physics and computational statistics literatures. I will describe the history of these walks and review some of the many results on the mixing properties of these processes. I then present some recent work of myself and Pillai, which uses connections to random matrix theory to obtain substantially improved bounds on the mixing times of these two walks.