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Markov model. In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. [1] It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property ). Generally, this assumption enables reasoning and computation with ...
A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game.
The prototypical Markov random field is the Ising model; indeed, the Markov random field was introduced as the general setting for the Ising model. [2] In the domain of artificial intelligence, a Markov random field is used to model various low- to mid-level tasks in image processing and computer vision. [3]
A more recent example is the Markov switching multifractal model of Laurent E. Calvet and Adlai J. Fisher, which builds upon the convenience of earlier regime-switching models. [99] [100] It uses an arbitrarily large Markov chain to drive the level of volatility of asset returns.
In statistics, Markov chain Monte Carlo ( MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution matches the target distribution.
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path —that results in a sequence of observed events. This is done especially in the context of Markov information sources and hidden Markov models (HMM).
Markov algorithm. In theoretical computer science, a Markov algorithm is a string rewriting system that uses grammar -like rules to operate on strings of symbols. Markov algorithms have been shown to be Turing-complete, which means that they are suitable as a general model of computation and can represent any mathematical expression from its ...
Markov decision process. In mathematics, a Markov decision process ( MDP) is a discrete-time stochastic control process. It provides a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying optimization problems solved via ...