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 ...

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 ...

The Applied Probability Trust is a non-profit publishing foundation established in 1964 to promote study and research in the mathematical sciences. Its titles Journal of Applied Probability and ...

Markov chains provide a fundamental framework for modelling stochastic processes, where the next state depends solely on the current state. Hidden Markov models (HMMs) extend this framework by ...

Consider a stochastic process X on a finite state space X = {1,..., d}. It is conditionally Markov, given a real-valued “input process” ζ. This is assumed to be small, which is modeled through the ...