T - 79 . 5204 Combinatorial Models and Stochastic Algorithms

Abstract

I Markov Chains and Stochastic Sampling 2 1 Markov Chains and Random Walks on Graphs . . . . . . . . . . . 2 1.1 Structure of Finite Markov Chains . . . . . . . . . . . . . 2 1.2 Existence and Uniqueness of Stationary Distribution . . . 10 1.3 Convergence of Regular Markov Chains . . . . . . . . . . 14 1.4 Transient Behaviour of General Chains . . . . . . . . . . 17 1.5 Reversible Markov Chains . . . . . . . . . . . . . . . . . 20 2 Markov Chain Monte Carlo Sampling . . . . . . . . . . . . . . . 22 3 Estimating the Convergence Rate of a Markov Chain . . . . . . . 26 3.1 Second Eigenvalue, Conductance, Canonical Paths . . . . 26 3.2 Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4 Exact Sampling with Coupled Markov Chains . . . . . . . . . . . 50

Cite this paper

@inproceedings{Orponen2007T7, title={T - 79 . 5204 Combinatorial Models and Stochastic Algorithms}, author={Pekka Orponen}, year={2007} }