Discretization of Continuous Markov Chains and Markov Chain Monte Carlo Convergence Assessment
该文展示了如何将连续状态空间的马尔可夫链严格离散化为有限马尔可夫链，并利用有限状态空间的收敛性质，基于Kemeny和Snell的散度准则评估MCMC收敛性，在三个标准例子上验证了效果。
Abstract We show that continuous state-space Markov chains can be rigorously discretized into finite Markov chains. The idea is to subsample the continuous chain at renewal times related to small sets that control the discretization. Once a finite Markov chain is derived from the Markov chain Monte Carlo output, general convergence properties on finite state spaces can be exploited for convergence assessment in several directions. Our choice is based on a divergence criterion derived from Kemeny and Snell, which is first evaluated on parallel chains with a stopping time and then implemented, more efficiently, on two parallel chains only, using Birkhoff's pointwise ergodic theorem for stopping rules. The performance of this criterion is illustrated on three standard examples.