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Figure 1. Probabilistic parameters of a hidden Markov model (example) X — states y — possible observations a — state transition probabilities b — output probabilities. In its discrete form, a hidden Markov process can be visualized as a generalization of the urn problem with replacement (where each item from the urn is returned to the original urn before the next step). [7]
A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game.
D. G. Champernowne built a Markov chain model of the distribution of income in 1953. [86] Herbert A. Simon and co-author Charles Bonini used a Markov chain model to derive a stationary Yule distribution of firm sizes. [87] Louis Bachelier was the first to observe that stock prices followed a random walk. [88]
For example, a series of simple observations, such as a person's location in a room, can be interpreted to determine more complex information, such as in what task or activity the person is performing. Two kinds of Hierarchical Markov Models are the Hierarchical hidden Markov model [2] and the Abstract Hidden Markov Model. [3]
The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected network of items. [1] An example of a model for such a field is the Ising model. A discrete ...
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
A hidden Markov model describes the joint probability of a collection of "hidden" and observed discrete random variables.It relies on the assumption that the i-th hidden variable given the (i − 1)-th hidden variable is independent of previous hidden variables, and the current observation variables depend only on the current hidden state.
The layered hidden Markov model (LHMM) is a statistical model derived from the hidden Markov model (HMM). A layered hidden Markov model (LHMM) consists of N levels of HMMs, where the HMMs on level i + 1 correspond to observation symbols or probability generators at level i. Every level i of the LHMM consists of K i HMMs running in parallel. [1]