An exact formula is presented for the probability of a specified frequency count of $m$-tuples $(m \geqq 1)$ in a sequence $X_1, X_2, \cdots, X_N$ from a Markov chain ...

What Is Markov Chain Monte Carlo? Markov Chain Monte Carlo (MCMC) is a powerful technique used in statistics and various scientific fields to sample from complex probability distributions. It is ...

With any Harris-recurrent Markov chain one can associate a sequence of random times at which the chain has the same distribution, and the chain can thereby be shown to be equivalent to one having a ...

Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. Queuing theory, terminology, and single queue systems are studied with ...

A Markov chain is a sequence of random variables that satisfies P(X t+1 ∣X t ,X t−1 ,…,X 1 )=P(X t+1 ∣X t ). Simply put, it is a sequence in which X t+1 depends only on X t and appears before X t−1 ...

In this episode probability mathematics and chess collide. In this episode probability mathematics and chess collide. What is the average number of steps it would take before a randomly moving knight ...

In 1987, Mark Jerrum (Queen Mary) and Alistair Sinclair (Berkley), both then at the University of Edinburgh, submitted a paper to the 13th Workshop on Graph-theoretic Concepts in Computer Science (WG) ...