The selection of a future state depends only on the current state in these objects, which consist of a set of states and a list of fixed transition probabilities.
Andrew Gelman and Don Rubin are advocates of the "multistart" technique for using these objects, which contrasts with the "one long run" approach. Algorithms that use Gibbs sampling store samples in one of these objects, from which they may discard data collected during the "burn-in" period. When applied to these objects, the Chapman–Kolmogorov equation reduces to an identity equivalent to matrix multiplication. One of these objects traverses a complicated probability distribution with the aid of an acceptance criterion in the Metropolis–Hastings algorithm. The selection of a future state depends only on the current state in these objects, which consist of a set of states and a list of fixed transition probabilities. For 10 points, identify these memoryless stochastic constructs used in namesake "Monte Carlo" algorithms, which are named for a Russian mathematician.
Andrew Gelman and Don Rubin are advocates of the "multistart" technique for using these objects, which contrasts with the "one long run" approach.
Markov chains [or Markov processes; accept Markov chain Monte Carlo algorithms; prompt on Markov or Markov models; prompt on MC or MCMC or MCMCMC] &lt;Other Science (Math)&gt;