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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 ...
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 ...
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 ...
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 "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.
The mixing time of a Markov chain is the number of steps needed for this convergence to happen, to a suitable degree of accuracy. 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 ...