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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. [104] Markov chains can be used structurally, as in Xenakis's Analogique A and B. [105] Markov chains are also used in systems which use a Markov model to react interactively to music input ...
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.
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 ...
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 ...
The term higher-order planning is often used to refer to marketing strategy since this strategy helps establish the general direction for the firm while providing a structure for the marketing program. [5] [6] Marketing Management is a combined effort of strategies on how a business can launch its products and services. On the other hand ...
Intuitively, a stochastic matrix represents a Markov chain; the application of the stochastic matrix to a probability distribution redistributes the probability mass of the original distribution while preserving its total mass. If this process is applied repeatedly, the distribution converges to a stationary distribution for the Markov chain.
The class of stochastic chains with memory of variable length was introduced by Jorma Rissanen in the article A universal data compression system. [1] Such class of stochastic chains was popularized in the statistical and probabilistic community by P. Bühlmann and A. J. Wyner in 1999, in the article Variable Length Markov Chains.
The "Markov" in "Markov decision process" refers to the underlying structure of state transitions that still follow the Markov property. The process is called a "decision process" because it involves making decisions that influence these state transitions, extending the concept of a Markov chain into the realm of decision-making under uncertainty.