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 ...

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 ...

This is a preview. Log in through your library . Abstract Let $\{X_n, n = 1, 2, \cdots\}$ be a Markov chain with finite state space $S = \{1, 2, \cdots, d ...

High-order Markov chain models extend the conventional framework by incorporating dependencies that span several previous states rather than solely the immediate past. This extension allows for a ...

The Annals of Statistics publishes research papers of the highest quality reflecting the many facets of contemporary statistics. Primary emphasis is placed on importance and originality, not on ...