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

Finite memory sources and variable-length Markov chains have recently gained popularity in data compression and mining, in particular, for applications in bioinformatics and language modelling. Here, ...

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 ...

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 ...

A Markov chain is a mathematical concept of a sequence of events, in which each future event depends only on the state of the previous events. Like most mathematical concepts, it has wide-ranging ...

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

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 evolution of DNA sequences can be described by discrete state continuous time Markov processes on a phylogenetic tree. We consider neighbor-dependent evolutionary models where the instantaneous ...