A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains
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This article is published in Annals of Mathematical Statistics.The article was published on 1970-02-01 and is currently open access. It has received 4618 citations till now. The article focuses on the topics: Examples of Markov chains & Markov chain.read more
Citations
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Probabilistic methods of identifying genes in prokaryotic genomes: Connections to the HMM theory
Rajeev K. Azad,Mark Borodovsky +1 more
TL;DR: It is shown that the Bayesian method implemented in GeneMark can be augmented and reintroduced as a rigorous forward-backward (FB) algorithm for local posterior decoding described in the HMM theory.
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Efficient genome ancestry inference in complex pedigrees with inbreeding
TL;DR: This article builds a hidden Markov model that derives the ancestry probabilities through inbreeding process without explicit modeling in every generation, and is accurate and fast, independent of the number of generations, for model animal resources such as the Collaborative Cross.
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A systolic neural network architecture for hidden Markov models
TL;DR: A programmable systolic array is proposed which maximizes the power of VLSI implementations in terms of intensive and pipelined computing and yet circumvents the limitation on communication.
Journal ArticleDOI
A discriminative training algorithm for hidden Markov models
Assaf Ben-Yishai,David Burshtein +1 more
TL;DR: A discriminative training algorithm for the estimation of hidden Markov model (HMM) parameters based on an approximation of the maximum mutual information (MMI) objective function and its maximization in a technique similar to the expectation-maximization (EM) algorithm is introduced.
Journal ArticleDOI
SA-Search: a web tool for protein structure mining based on a Structural Alphabet.
TL;DR: SA-Search is a web tool that can be used to mine for protein structures and extract structural similarities using a hidden Markov model derived Structural Alphabet that allows the compression of three-dimensional protein conformations into a one-dimensional representation using a limited number of prototype conformations.
References
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Journal ArticleDOI
Statistical Inference for Probabilistic Functions of Finite State Markov Chains
Leonard E. Baum,Ted Petrie +1 more
Journal ArticleDOI
An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology
Leonard E. Baum,J. A. Eagon +1 more
TL;DR: In this paper, a polynomial with nonnegative coefficients homogeneous of degree d in its variables is shown to be polynomially homogeneous unless 3(3(x))>P(x), where 3(x)=x.
Book ChapterDOI
The Gamma Function
Willi Freeden,Martin Gutting +1 more
TL;DR: The Gamma function as discussed by the authors is a generalized factorial function that can be used to estimate the probability distribution of a probability distribution, and it has been used in many applications, e.g., as part of probability distributions.