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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.
Hidden Markov model; Hidden Markov random field; Hidden semi-Markov model; Hierarchical Bayes model; Hierarchical clustering; Hierarchical hidden Markov model; Hierarchical linear modeling; High-dimensional statistics; Higher-order factor analysis; Higher-order statistics; Hirschman uncertainty; Histogram; Historiometry; History of randomness ...
Stephen L. Parente (1995) implemented a Markov Chain to model economic growth across different countries given different technological barriers. [ 7 ] In Product marketing , Warren Schirtzinger proposed an expansion of the original lifecycle (the Customer Alignment Lifecycle [ 8 ] ) which describes the configuration of five different business ...
A family of Markov chains is said to be rapidly mixing if the mixing time is a polynomial function of some size parameter of the Markov chain, and slowly mixing otherwise. This book is about finite Markov chains, their stationary distributions and mixing times, and methods for determining whether Markov chains are rapidly or slowly mixing. [1] [4]
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
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.