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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Pattern analysis in branching and axillary flowering sequences.
TL;DR: The primary aim of the proposed analysis methods is to reveal patterns not directly apparent in the data, and thus to deepen the biological understanding of the underlying mechanisms that control the branching and the axillary flowering of plants over time and space.
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Asymptotics of the maximum likelihood estimator for general hidden Markov models
Randal Douc,Catherine Matias +1 more
TL;DR: In this article, the authors consider the consistency and asymptotic normality of the maximum likelihood estimator for a possibly non-stationary hidden Markov model where the hidden state space is a separable and compact space not necessarily finite, and both the transition kernel of the hidden chain and the conditional distribution of the observations depend on a parameter.
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The mean field theory in EM procedures for blind Markov random field image restoration
TL;DR: A Markov random field model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described, and results show that this approach provides good blur estimates and restored images.
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Automatic recognition and understanding of spoken language - a first step toward natural human-machine communication
Bing-Hwang Juang,Sadaoki Furui +1 more
TL;DR: An accurate overview of spoken language technology is presented as a basis to inspire future advances and the limitations of the current technology are discussed, and the challenges that are ahead are pointed out.
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On adaptive decision rules and decision parameter adaptation for automatic speech recognition
Chin-Hui Lee,Qiang Huo +1 more
TL;DR: The mathematical framework for Bayesian adaptation of acoustic and language model parameters is first described, and maximum a posteriori point estimation is developed for hidden Markov models and a number of useful parameters densities commonly used in automatic speech recognition and natural language processing.
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.