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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An introduction to MCMC for machine learning
TL;DR: This purpose of this introductory paper is to introduce the Monte Carlo method with emphasis on probabilistic machine learning and review the main building blocks of modern Markov chain Monte Carlo simulation.
Journal ArticleDOI
The expectation-maximization algorithm
TL;DR: The EM (expectation-maximization) algorithm is ideally suited to problems of parameter estimation, in that it produces maximum-likelihood (ML) estimates of parameters when there is a many-to-one mapping from an underlying distribution to the distribution governing the observation.
Journal ArticleDOI
Next-generation genotype imputation service and methods.
Sayantan Das,Lukas Forer,Sebastian Schönherr,Carlo Sidore,Carlo Sidore,Adam E. Locke,Alan Kwong,Scott I. Vrieze,Emily Y. Chew,Shawn Levy,Matt McGue,David Schlessinger,Dwight Stambolian,Po-Ru Loh,William G. Iacono,Anand Swaroop,Laura J. Scott,Francesco Cucca,Florian Kronenberg,Michael Boehnke,Gonçalo R. Abecasis,Christian Fuchsberger,Christian Fuchsberger,Christian Fuchsberger +23 more
TL;DR: Improvements to imputation machinery are described that reduce computational requirements by more than an order of magnitude with no loss of accuracy in comparison to standard imputation tools.
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Maximum a posteriori estimation for multivariate Gaussian mixture observations of Markov chains
Jean-Luc Gauvain,Chin-Hui Lee +1 more
TL;DR: A framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented, and Bayesian learning is shown to serve as a unified approach for a wide range of speech recognition applications.
Journal ArticleDOI
Analysis of time series subject to changes in regime
TL;DR: An EM algorithm for obtaining maximum likelihood estimates of parameters for processes subject to discrete shifts in autoregressive parameters, with the shifts themselves modeled as the outcome of a discrete-valued Markov process is introduced.
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.