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Hidden Markov model. A hidden Markov model ( HMM) is a Markov model in which the observations are dependent on a latent (or "hidden") Markov process (referred to as ). An HMM requires that there be an observable process whose outcomes depend on the outcomes of in a known way.
The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm .
Baum–Welch algorithm. In electrical engineering, statistical computing and bioinformatics, the Baum–Welch algorithm is a special case of the expectation–maximization algorithm used to find the unknown parameters of a hidden Markov model (HMM). It makes use of the forward-backward algorithm to compute the statistics for the expectation step.
Markov model. In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. [1] It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property ). Generally, this assumption enables reasoning and computation with ...
Forward–backward algorithm. The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions , i.e. it computes, for all hidden state variables , the distribution . This inference task is usually called smoothing.
D. G. Champernowne built a Markov chain model of the distribution of income in 1953. Herbert A. Simon and co-author Charles Bonini used a Markov chain model to derive a stationary Yule distribution of firm sizes. Louis Bachelier was the first to observe that stock prices followed a random walk.
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path —that results in a sequence of observed events. This is done especially in the context of Markov information sources and hidden Markov models (HMM).
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. An example of a model for such a field is the Ising model.