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
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Automated Detection of Influenza Epidemics with Hidden Markov Models
TL;DR: The method uses Hidden Markov Models with an Exponential-Gaussian mixture to characterize the non-epidemic and epidemic dynamics in a time series of influenza-like illness incidence rates to reduce the number of false detections and increase robustness to variations in the data.
Journal ArticleDOI
Maximum-likelihood parameter estimation of bilinear systems
TL;DR: The emphasis here is on developing practical methods that are illustrated to be numerically reliable, robust to choice of initialization point, and numerically efficient in terms of how computation and memory requirements scale relative to problem size.
Journal ArticleDOI
Analysis, classification, and coding of multielectrode spike trains with hidden Markov models
TL;DR: It is shown that hidden Markov models (HMMs) are a powerful tool in the analysis of multielectrode data for a 30-electrode measurement of neuronal spike activity in the monkey's visual cortex during the application of different visual stimuli.
Journal ArticleDOI
Markovian arrival process parameter estimation with group data
TL;DR: A numerical procedure for fitting a MAP and a Markov-modulated Poisson process (MMPP) to group data and provides an efficient approximation based on the proposed EM algorithm for the MMPP estimation.
Journal ArticleDOI
Copy number variation detection using next generation sequencing read counts.
Heng Wang,Dan Nettleton,Kai Ying +2 more
TL;DR: This work proposes a new methodology for detecting CNVs using NGS data based on a hidden Markov model with emission probabilities that are governed by mixture distributions, and uses the Expectation-Maximization algorithm to estimate the parameters in the model.
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.