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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]
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]
Markov chain. Examples of Markov chains; Detailed balance; Markov property; Hidden Markov model; Maximum-entropy Markov model; Markov chain mixing time; Markov partition; Markov process. Continuous-time Markov process; Piecewise-deterministic Markov process; Martingale. Doob martingale; Optional stopping theorem; Martingale representation ...
Layered hidden Markov model; Le Cam's theorem; Lead time bias; Least absolute deviations; Least-angle regression; Least squares; Least-squares spectral analysis; Least squares support vector machine; Least trimmed squares; Learning theory (statistics) Leftover hash-lemma; Lehmann–Scheffé theorem; Length time bias; Levene's test; Level of ...
Hidden Markov models (8 P) M. Markov networks (8 P) Pages in category "Markov models" The following 62 pages are in this category, out of 62 total. ... Examples of ...
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 hierarchical hidden Markov model (HHMM) is a statistical model derived from the hidden Markov model (HMM). In an HHMM, each state is considered to be a self-contained probabilistic model. More precisely, each state of the HHMM is itself an HHMM. HHMMs and HMMs are useful in many fields, including pattern recognition. [1] [2]
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]