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 ...

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 ...

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 ...

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 ...

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) ...

Amid all the hype about AI it sometimes seems as though the world has lost sight of the fact that software such as ChatGPT contains no intelligence. Instead it’s an extremely sophisticated system for ...