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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Interpretation and inference in mixture models: Simple MCMC works
TL;DR: The mixture model likelihood function is invariant with respect to permutation of the components of the mixture, and simple and widely used Markov chain Monte Carlo algorithms with data augmentation reliably recover the entire posterior distribution.
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Simultaneously recorded single units in the frontal cortex go through sequences of discrete and stable states in monkeys performing a delayed localization task.
TL;DR: In this later period, conventional methods such as the PSTH cannot detect any firing rate modulations, but the HMM successfully captures transitions between distinct states that are specific to the monkey's behavioral response and occur at highly variable times from trial to trial.
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Qualitative recognition of motion using temporal texture
Randal C. Nelson,R. Polana +1 more
TL;DR: It is shown that certain statistical spatial and temporal features that can be derived from approximations to the motion field have invariant properties, and can be used to classify regional activities such as windblown trees, ripples on water, or chaotic fluid flow, that are characterized by complex, nonrigid motion.
Segmentation of heart sound recordings by a duration dependent Hidden Markov Model
TL;DR: The results indicate that the DHMM is an appropriate model of the heart cycle and suitable for segmentation of clinically recorded heart sounds.
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Measuring self-regulated learning skills through social interactions in a teachable agent environment
TL;DR: Methods that are employed for detecting and characterizing students' behavior patterns from their activity sequences on the system are discussed, and a method for learning hidden Markov models (HMM) from the activity logs is discussed.
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.