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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 ...
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.
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 ...
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 stochastic matrix was developed alongside the Markov chain by Andrey Markov, a Russian mathematician and professor at St. Petersburg University who first published on the topic in 1906. [3] His initial intended uses were for linguistic analysis and other mathematical subjects like card shuffling , but both Markov chains and matrices rapidly ...
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 more steps ...
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix.