MATH 396 A: Finite Markov Chains and Monte-Carlo Methods

Finite Markov chains; stationary distributions; time reversals; classification of states; classical Markov chains; convergence in total variation distance and L2; spectral analysis; relaxation time; Monte Carlo techniques: rejection sampling, Metropolis-Hastings, Gibbs sampler, Glauber dynamics, hill climb and simulated annealing; harmonic functions and martingales for Markov chains. Prerequisite: a minimum grade of 2.0 in MATH 208; and either a minimum grade of 2.0 in MATH 394/STAT 394 and STAT 395/MATH 395, or a minimum grade of 2.0 in STAT 340 and STAT 341, or a minimum grade of 2.0 in STAT 340 and STAT 395/MATH 395. Offered: jointly with STAT 396; Sp.