Discover how Markov chains predict real systems, from Ulam and von Neumann’s Monte Carlo to PageRank, so you can grasp ...

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 ...

A Markov Chain is a sequence of random values whose probabilities at a time interval depends upon the value of the number at the previous time. A Markov Chain is a sequence of random values whose ...

Markov Chain Monte Carlo (MCMC) methods have become indispensable in contemporary statistical science, enabling researchers to approximate complex probability distributions that are otherwise ...

We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic ...

This course is compulsory on the MSc in Operations Research & Analytics. This course is not available as an outside option to students on other programmes. The course covers theory including the ...

We build optimal exponential bounds for the probabilities of large deviations of sums $\sum_{k=1}^n f(X_k)$ where (Xk) is a finite reversible Markov chain and f is an arbitrary bounded function. These ...