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These higher-order chains tend to generate results with a sense of phrasal structure, rather than the 'aimless wandering' produced by a first-order system. [97] Markov chains can be used structurally, as in Xenakis's Analogique A and B. [98] Markov chains are also used in systems which use a Markov model to react interactively to music input. [99]
In the mathematical theory of stochastic processes, variable-order Markov (VOM) models are an important class of models that extend the well known Markov chain models. In contrast to the Markov chain models, where each random variable in a sequence with a Markov property depends on a fixed number of random variables, in VOM models this number of conditioning random variables may vary based on ...
A Tolerant Markov model (TMM) is a probabilistic-algorithmic Markov chain model. [6] It assigns the probabilities according to a conditioning context that considers the last symbol, from the sequence to occur, as the most probable instead of the true occurring symbol. A TMM can model three different natures: substitutions, additions or deletions.
A Markov chain with two states, A and E. In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past.
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.
Markov chain; Markov chain central limit theorem; Markov chain geostatistics; Markov chain Monte Carlo; Markov partition; Markov property; Markov switching multifractal; Markovian discrimination; Maximum-entropy Markov model; MegaHAL; Models of DNA evolution; MRF optimization via dual decomposition; Multiple sequence alignment
The process is Markovian only at the specified jump instants, justifying the name semi-Markov. [1] [2] [3] (See also: hidden semi-Markov model.) A semi-Markov process (defined in the above bullet point) in which all the holding times are exponentially distributed is called a continuous-time Markov chain. In other words, if the inter-arrival ...
If () = is the unit function and =, the interaction between the particle vanishes and the particle model reduces to a sequence of independent copies of the Markov chain . When ϵ = 0 {\displaystyle \epsilon =0} the mean field particle model described above reduces to a simple mutation-selection genetic algorithm with fitness function G and ...