31. In Markov chains, a coarse Markov chain may be obtained by aggregating states. 32. P Fold values are computed using the first step analysis of Markov chain theory. 33. I would be interested in seeing the the result of the Markov Chain analysis. 34. Frequently, these problems will then be reduced to others involving independent Markov chains . 35. A primary subject of his research later became known as Markov chains and Markov processes. 36. An irreducible Markov chain only needs one aperiodic state to imply all states are aperiodic. 37. A random walk on a graph is a very special case of a Markov chain . 38. Modern potential theory is also intimately connected with probability and the theory of Markov chains . 39. He also showed that noise can speed up the convergence of Markov chains to equilibrium. 40. This analysis may be implemented using the Markov chain Monte Carlo ( MCMC ) method.
