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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 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.
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 chains are used in various areas of biology. Notable examples include: ... [107] to hidden Markov models combined with wavelets, [106] ...
A profile hidden Markov model (HMM) modelling a multiple sequence alignment. A hidden Markov model (HMM) is a probabilistic model that can assign likelihoods to all possible combinations of gaps, matches, and mismatches, to determine the most likely MSA or set of possible MSAs. HMMs can produce a single highest-scoring output but can also ...
XRATE is a program for prototyping phylogenetic hidden Markov models and stochastic context-free grammars. [1] [2] It is used to discover patterns of evolutionary conservation in sequence alignments. The program can be used to estimate parameters for such models from "training" alignment data, or to apply the parameterized model so as to ...
In statistics, a hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field. Suppose that we observe a random variable , where .
The SUPERFAMILY annotation is based on a collection of hidden Markov models (HMM), which represent structural protein domains at the SCOP superfamily level. [12] [13] A superfamily groups together domains which have an evolutionary relationship.