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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 ...
The hierarchical hidden Markov model (HHMM) is a statistical model derived from the hidden Markov model (HMM). In an HHMM, each state is considered to be a self-contained probabilistic model. More precisely, each state of the HHMM is itself an HHMM. HHMMs and HMMs are useful in many fields, including pattern recognition.
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 ...
A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or "hidden") Markov process (referred to as ). An HMM requires that there be an observable process Y {\displaystyle Y} whose outcomes depend on the outcomes of X {\displaystyle X} in a known way.
D. G. Champernowne built a Markov chain model of the distribution of income in 1953. Herbert A. Simon and co-author Charles Bonini used a Markov chain model to derive a stationary Yule distribution of firm sizes. Louis Bachelier was the first to observe that stock prices followed a random walk.
Birth–death process. The birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one. It was introduced by William Feller. [1]
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.
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 ...
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