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 ...

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 are mathematical models describing sequences of events in which the probability of each future state depends solely on the present state. Random walks constitute a prominent subclass in ...

From Plato's perfect forms to Markov's state machines, the deepest question in probability isn't whether randomness exists, but whether it secretly follows rules. This is the story of how dependent ...

Here’s a game Claude Shannon, the founder of information theory, invented in 1948. He was trying to model the English language as a random process. Go to your bookshelf, pick up a random book, open it ...

Online bipartite matching (OBM) has a rich history in the literature of online algorithms, where it has been an influential problem inspiring many algorithms and techniques. This problem of obtaining ...