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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Journal ArticleDOI
A hierarchical mixture model for clustering three-way data sets
TL;DR: The proposed extension is obtained by adapting the multilevel latent class model for categorical responses to the three-way situation, as well as to the situation in which responses include continuous variables.
Proceedings ArticleDOI
Estimation of hidden Markov model parameters by minimizing empirical error rate
TL;DR: An approach for designing a set of acoustic models for speech recognition applications which results in a minimal empirical error rate for a given decoder and training data is studied and hidden Markov models are used to characterize the probability density functions of the acoustic signals from the different words in the vocabulary.
Journal ArticleDOI
Longitudinal analysis of self-reported health status by mixture latent auto-regressive models
TL;DR: In this paper, a latent process is modelled by a mixture of auto-regressive AR(1) processes with different means and correlation coefficients, but with equal variances.
Journal ArticleDOI
Clustering Multivariate Longitudinal Observations: The Contaminated Gaussian Hidden Markov Model
Antonio Punzo,Antonello Maruotti +1 more
TL;DR: The contaminated Gaussian HMM is introduced and the effectiveness of the proposed model in comparison with HMMs of different elliptical distributions is demonstrated, and the performance of some well-known information criteria in selecting the true number of latent states is evaluated.
Journal ArticleDOI
Prediction of ozone levels using a Hidden Markov Model (HMM) with Gamma distribution
TL;DR: In this article, the authors proposed a method based on a HMM with a Gamma distribution (HMM-Gamma) where each monitoring day is pre-labeled according to its maximum 8-h average ozone concentration and monitoring days are further grouped into zones with different ozone levels.
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.