What is Markov chain?

  • (noun): A Markov process for which the parameter is discrete time values.
    Synonyms: Markoff chain

Markov Chain

A Markov chain, named after Andrey Markov, is a mathematical system that undergoes transitions from one state to another, between a finite or countable number of possible states. It is a random process usually characterized as memoryless: the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property. Markov chains have many applications as statistical models of real-world processes.

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Some articles on Markov chain:

Markov Chain - History
... Andrey Markov produced the first results (1906) for these processes, purely theoretically ... Markov chains are related to Brownian motion and the ergodic hypothesis, two topics in physics which were important in the early years of the twentieth century, but Markov ... Seneta provides an account of Markov's motivations and the theory's early development ...
Balance Equation - Global Balance
... in principle can always be solved to give the equilibrium distribution of a Markov chain (when such a distribution exists) ... For a Markov chain with state space S, transition rate from state i to j given by qij and equilibrium distribution given by, the global balance equations are given for ... For a discrete time Markov chain with transition matrix P and equilibrium distribution the global balance equation is ...
Nonlinear Dimensionality Reduction - Manifold Learning Algorithms - Diffusion Maps
... the relationship between heat diffusion and a random walk (Markov Chain) an analogy is drawn between the diffusion operator on a manifold and a Markov transition ... see here that from the tuple {X,k} one can construct a reversible Markov Chain ... If has to faithfully represent a Markov matrix, then it has to be normalized by the corresponding degree matrix now represents a Markov chain ...
Prediction Suffix Tree
... The concept of the Markov chain of order L, which we essentially owe to the Russian mathematician Andrej Andreevic Markov (1907), has two drawbacks ... of parameters of the model grows exponentially with the order L of the chain ... Willems - 1995) was the Variable Length Markov chain (Buhlmann - 1999) ...
Multiple-try Metropolis
... In Markov chain Monte Carlo, the Metropolis–Hastings algorithm (MH) can be used to sample from a probability distribution which is difficult to sample from directly ... On the other hand, if is too small, almost all steps will be accepted, and the Markov chain will be similar to a random walk through the probability space ... In this event, the Markov Chain will not fully explore the probability space in any reasonable amount of time ...

Famous quotes containing the word chain:

    The years seemed to stretch before her like the land: spring, summer, autumn, winter, spring; always the same patient fields, the patient little trees, the patient lives; always the same yearning; the same pulling at the chain—until the instinct to live had torn itself and bled and weakened for the last time, until the chain secured a dead woman, who might cautiously be released.
    Willa Cather (1873–1947)