Markov chains to sample in Monte Carlo methods, useful for Bayesian inference
Convergence results (Ergodic theorems, etc) can be shown using results in Discrete-time Markov chain
Measure of convergence: Gelman and Rubin’s , but must start the ensemble of walkers/chains well dispersed on the sampling space.
Performance of samplers: number of effective samples per unit time. Need effective sample size (number of samples that need to pass so that the new sample is approx independent). We are interested on this because independence samplers often converge to the stationary distribution faster. However, Antithetic sampling (where new samples are anti-correlated to current samples) can converge faster than independence sampling! Can estimate effective sample size experimentally.. any theroy?
Stan programming language