The purpose of the study is to use the expectation-maximization (em) algorithm for finding the maximum likelihood estimates (MLEs) under the normal mixture models in which allow heterogeneity in forms of the multi-nod...
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ISBN:
(纸本)9781538623176
The purpose of the study is to use the expectation-maximization (em) algorithm for finding the maximum likelihood estimates (MLEs) under the normal mixture models in which allow heterogeneity in forms of the multi-nodes, skewed, long-tailed, and/or contaminated distributions. The motivational application of the standardized morbidity ratio (SMR) of geographical HIV/AIDS data displaying on a map among all study provinces in Thailand 2013 is illustrated. The results showed that the normal mixture model fitted data well with the nice MLEs corresponding to the em algorithm coping with good yielding both numerically stable convergence and the fine estimates of local maximum points. Another advantage of em algorithm was in adding up the latent unobserved probabilities of each study province belonging to the component of normal mixture in solving the problem of the incomplete data while other algorithms, such as Newton-Raphson and Fisher Scoring, couldn't be able to augment those unobserved missing data. However, em algorithm seemed to have slow convergence.
The estimation and detection of a weak magnetic dipole signal is a critical problem in magnetic target detection. The difficulty arises due to a latent variable in the model, which affects the estimation and detection...
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The estimation and detection of a weak magnetic dipole signal is a critical problem in magnetic target detection. The difficulty arises due to a latent variable in the model, which affects the estimation and detection performance, especially at low signal-to-noise ratios (SNRs). A non-probability-distribution expectation maximization (NPD-em) algorithm is proposed to estimate the magnetic dipole signal with the latent variable at low SNRs. A reasonable value of an intermediate variable instead of the optimal one is determined without any probability information in the iteration of the NPD-em algorithm, which overcomes an unknown probability distribution appearing in the traditional expectation maximization (em) algorithm and reduces the calculated amount by 3 orders of magnitude compared with the traditional em algorithm. A statistic based on the NPD-em algorithm representing an unbiased estimator of the target signal energy is constructed to detect the magnetic dipole signal at low SNRs, and an innovative compensation in the detector is introduced so as to reduce the noise influence on the statistic. The experiment results show that, the constructed detector is comparable to the ideal matching filter due to the attractive performance of the NPD-em algorithm and the outstanding statistic.
We study properties and parameter estimation of a finite-state, homogeneous, continuous-time, bivariate Markov chain. Only one of the two processes of the bivariate Markov chain is assumed observable. The general form...
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We study properties and parameter estimation of a finite-state, homogeneous, continuous-time, bivariate Markov chain. Only one of the two processes of the bivariate Markov chain is assumed observable. The general form of the bivariate Markov chain studied here makes no assumptions on the structure of the generator of the chain. Consequently, simultaneous jumps of the observable and underlying processes are possible, neither process is necessarily Markov, and the time between jumps of each of the two processes has a phase-type distribution. Examples of bivariate Markov chains include the Markov modulated Poisson process and the batch Markovian arrival process when appropriate modulo counts are used in each case. We develop an expectation-maximization (em) procedure for estimating the generator of a bivariate Markov chain, and we demonstrate its performance. The procedure does not rely on any numerical integration or sampling scheme of the continuous-time bivariate Markov chain. The proposed em algorithm is equally applicable to multivariate Markov chains. (C) 2012 Elsevier B.V. All rights reserved.
Application of the em (Expectation-Maximization) algorithm to sequence estimation in an unknown channel can in principle produce MLSE (maximum likelihood sequence estimates) that are not dependent on a particular chan...
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Application of the em (Expectation-Maximization) algorithm to sequence estimation in an unknown channel can in principle produce MLSE (maximum likelihood sequence estimates) that are not dependent on a particular channel estimate. The Expectation step of this algorithm cannot be directly performed for continuous phase modulated (CPM) signals transmitted in a time varying multipath channel. We therefore derive a simplification of the em algorithm for CPM signals in this channel. Simulations applied to the Global System for Mobile Communications (GSM) show that the simplified em algorithm significantly decreases the amount of training data needed for the channel model considered, and removes the majority of the bit errors that are due to imperfect knowledge of the channel.
In this paper, a distributed expectation maximization (Dem) algorithm is first introduced in a general form for estimating the parameters of a finite mixture of components. This algorithm is used for density estimatio...
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In this paper, a distributed expectation maximization (Dem) algorithm is first introduced in a general form for estimating the parameters of a finite mixture of components. This algorithm is used for density estimation and clustering of data distributed over nodes of a network. Then, a distributed incremental em algorithm (DIem) with a higher convergence rate is proposed. After a full derivation of distributed em algorithms, convergence of these algorithms is analyzed based on the negative free energy concept used in statistical physics. An analytical approach is also developed for evaluating the convergence rate of both incremental and distributed incremental em algorithms. It is analytically shown that the convergence rate of DIem is much faster than that of the Dem algorithm. Finally, simulation results approve that DIem remarkably outperforms Dem for both synthetic and real data sets.
An expectation maximization (em) algorithm is presented for ARX modeling with uncertain communication channels. The considered model consists of two parts: a dynamic model which is expressed by an ARX model, and an ou...
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An expectation maximization (em) algorithm is presented for ARX modeling with uncertain communication channels. The considered model consists of two parts: a dynamic model which is expressed by an ARX model, and an output model, both subject to white Gaussian noises. Since the true outputs of the ARX model are assumed to be unknown, a modified Kalman filter is derived to estimate the output, and then the parameters are estimated by the em algorithm using the estimated outputs. The Kullback-Leibler divergence and the submartingale are used to prove that the parameter estimates can converge to the true values with the em algorithm. Furthermore, a simulation example is presented to verify the theoretical results. (C) 2020 Elsevier B.V. All rights reserved.
An approach is proposed for initializing the expectation-maximization (em) algorithm in multivariate Gaussian mixture models with an unknown number of components. As the em algorithm is often sensitive to the choice o...
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An approach is proposed for initializing the expectation-maximization (em) algorithm in multivariate Gaussian mixture models with an unknown number of components. As the em algorithm is often sensitive to the choice of the initial parameter vector, efficient initialization is an important preliminary process for the future convergence of the algorithm to the best local maximum of the likelihood function. We propose a strategy initializing mean vectors by choosing points with higher concentrations of neighbors and using a truncated normal distribution for the preliminary estimation of dispersion matrices. The suggested approach is illustrated on examples and compared with several other initialization methods. (C) 2011 Elsevier B.V. All rights reserved.
Using a theory of list-mode maximum-likelihood (ML) source reconstruction presented recently by Barrett et al. [1], this paper formulates a corresponding expectation-maximization (em) algorithm, as well as a method fo...
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Using a theory of list-mode maximum-likelihood (ML) source reconstruction presented recently by Barrett et al. [1], this paper formulates a corresponding expectation-maximization (em) algorithm, as well as a method for estimating noise properties at the ML estimate, List-mode ML is of interest in cases where the dimensionality of the measurement space impedes a binning of the measurement data. It can be advantageous in cases where a better forward model can be obtained by including more measurement coordinates provided by a given detector. Different figures of merit for the detector performance can be computed from the Fisher information matrix (FIM). This paper uses the observed FIM, which requires a single data set, thus, avoiding costly ensemble statistics, The proposed techniques are demonstrated for an idealized two-dimensional (2-D) positron emission tomography (PET) [2-D PET] detector. We compute from simulation data the improved image quality obtained by including the time of flight of the coincident quanta.
Markovian binary trees form a class of continuous-time branching processes where the lifetime and reproduction epochs of individuals are controlled by an underlying Markov process. An Expectation Maximization (em) alg...
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Markovian binary trees form a class of continuous-time branching processes where the lifetime and reproduction epochs of individuals are controlled by an underlying Markov process. An Expectation Maximization (em) algorithm is developed to estimate the parameters of the Markov process from the continuous observation of some populations, first with information about which individuals reproduce or die (the distinguishable case), and second without this information (the indistinguishable case). The performance of the em algorithm is illustrated with some numerical examples. Fits resulting from the distinguishable case are shown not to be significantly better than fits resulting from the indistinguishable case using some goodness of fit measures. (C) 2013 Elsevier B.V. All rights reserved.
This paper describes an implementation of the em algorithm for the statistical analysis of a finite mixture of distributions arising when data are censored but partially identifiable. We consider a scheme of type I ce...
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This paper describes an implementation of the em algorithm for the statistical analysis of a finite mixture of distributions arising when data are censored but partially identifiable. We consider a scheme of type I censoring where censoring times are random. The estimation of standard errors proposed by Meng and Rubin (1991. Using em to obtain asymptotic variance-covariance matrices: the Sem algorithm. J. Amer. Statist. Assoc. 86(416), 899-909) is also implemented in the context of the above mixture. A Bayesian method introduced in Contreras-Cristan et al. (2003. Statistical inference for mixtures of distributions for censored data with partial identification. Commun. in Statist. Theory Methods 32(4), 749-774) for the case of a constant censoring value is extended to the case of random censoring times. Comparisons with different methods are carried out both with simulated data and with the observations on failure times for communication transmitter-receivers of Mendenhall and Hader (1958. Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data. Biometrika 45, 504-520). (c) 2006 Elsevier B.V. All rights reserved.
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