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.
Studies/trials assessing status and progression of periodontal disease (PD) usually focus on quantifying the relationship between the clustered (tooth within subjects) bivariate endpoints, such as probed pocket depth ...
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Studies/trials assessing status and progression of periodontal disease (PD) usually focus on quantifying the relationship between the clustered (tooth within subjects) bivariate endpoints, such as probed pocket depth (PPD), and clinical attachment level (CAL) with the covariates. Although assumptions of multivariate normality can be invoked for the random terms (random effects and errors) under a linear mixed model (LMM) framework, violations of those assumptions may lead to imprecise inference. Furthermore, the response-covariate relationship may not be linear, as assumed under a LMM fit, and the regression estimates obtained therein do not provide an overall summary of the risk of PD, as obtained from the covariates. Motivated by a PD study on Gullah-speaking African-American Type-2 diabetics, we cast the asymmetric clustered bivariate (PPD and CAL) responses into a non-linear mixed model framework, where both random terms follow the multivariate asymmetric Laplace distribution (ALD). In order to provide a one-number risk summary, the possible non-linearity in the relationship is modeled via a single-index model, powered by polynomial spline approximations for index functions, and the normal mixture expression for ALD. To proceed with a maximum-likelihood inferential setup, we devise an elegant em-type algorithm. Moreover, the large sample theoretical properties are established under some mild conditions. Simulation studies using synthetic data generated under a variety of scenarios were used to study the finite-sample properties of our estimators, and demonstrate that our proposed model and estimation algorithm can efficiently handle asymmetric, heavy-tailed data, with outliers. Finally, we illustrate our proposed methodology via application to the motivating PD study.
In this article, using longitudinal data, we develop the theory of credibility by copula model. The convex combination of copulas is used to describe the dependencies among claims. Finally, for comparing with the resu...
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In this article, using longitudinal data, we develop the theory of credibility by copula model. The convex combination of copulas is used to describe the dependencies among claims. Finally, for comparing with the results of a single copula, using em algorithm, some simulations of Massachusetts automobile claims are presented.
A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric ***,data that arise from a heterogeneous population can be efficiently a...
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A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric ***,data that arise from a heterogeneous population can be efficiently analysed by a finite mixture of regression *** observations motivate us to propose a novel finite mixture of median regression model based on a mixture of the skew-normal distributions to explore asymmetrical data from several *** the appropriate choice of the tuning parameters,we establish the theoretical properties of the proposed procedure,including consistency for variable selection method and the oracle property in estimation.A productive nonparametric clustering method is applied to select the number of components,and an efficient em algorithm for numerical computations is *** studies and a real data set are used to illustrate the performance of the proposed methodologies.
Iterative minimization algorithms appear in various areas including machine learning, neural networks, and information theory. The em algorithm is one of the famous iterative minimization algorithms in the area of mac...
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Iterative minimization algorithms appear in various areas including machine learning, neural networks, and information theory. The em algorithm is one of the famous iterative minimization algorithms in the area of machine learning, and the Arimoto-Blahut algorithm is a typical iterative algorithm in the area of information theory. However, these two topics had been separately studied for a long time. In this paper, we generalize an algorithm that was recently proposed in the context of the Arimoto-Blahut algorithm. Then, we show various convergence theorems, one of which covers the case when each iterative step is done approximately. Also, we apply this algorithm to the target problem of the em algorithm, and propose its improvement. In addition, we apply it to other various problems in information theory.
Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are objects of different types. One field of application of such models in biology is in studies of cell prolifera...
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ISBN:
(纸本)9783319086729;9783319086712
Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are objects of different types. One field of application of such models in biology is in studies of cell proliferation. A sampling scheme that appears frequently is observing the cell count in several independent colonies at discrete time points (sometimes only one). Thus, the process is not observable in the sense of the whole tree, but only as the "generation" at given moment in time, which consist of the number of cells of every type. This requires an em-type algorithm to obtain a maximum likelihood (ML) estimation of the parameters of the branching process. A computational approach for obtaining such estimation of the offspring distribution is presented in the class of Markov branching processes with terminal types.
In the standard minimum-variance filter recursions it is routinely assumed that the noises are zero-mean and white. In image restoration applications, the data can be contaminated with (non-zero-mean) Poisson noise. T...
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ISBN:
(纸本)9781479949755
In the standard minimum-variance filter recursions it is routinely assumed that the noises are zero-mean and white. In image restoration applications, the data can be contaminated with (non-zero-mean) Poisson noise. This paper introduces the minimum-variance filter for the case where the measurement noise includes a Poisson-distributed component. An em algorithm for estimating the Poisson noise intensity is described. Conditions for the convergence of the algorithms are also investigated. An image restoration example is presented which demonstrates the efficacy of the described method.
This paper proposes the estimation of a smooth graphon model for network data analysis using principles of the em algorithm. The approach considers both variability with respect to ordering the nodes of a network and ...
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This paper proposes the estimation of a smooth graphon model for network data analysis using principles of the em algorithm. The approach considers both variability with respect to ordering the nodes of a network and smooth estimation of the graphon by nonparametric regression. To do so, (linear) B-splines are used, which allow for smooth estimation of the graphon, conditional on the node ordering. This provides the M-step. The true ordering of the nodes arising from the graphon model remains unobserved and MCMC techniques are employed to obtain position samples conditional on the network. This yields the E-step. Combining both steps gives an em based approach for smooth graphon estimation. Unlike common other methods, this procedure does not require the restriction of a monotonic marginal function. The proposed graphon estimate allows to explore node-ordering strategies and therefore to compare the common degree-based node ranking with the ordering conditional on the network. Variability and uncertainty are taken into account relying on the MCMC sequences. Examples and simulation studies support the applicability of the approach.
A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objec...
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A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve multiple-step-ahead predictions. The common mean process is defined as a GP for which the hyper-posterior distribution is tractable. Therefore an em algorithm is derived for handling both hyper-parameters optimisation and hyper-posterior computation. Unlike previous approaches in the literature, the model fully accounts for uncertainty and can handle irregular grids of observations while maintaining explicit formulations, by modelling the mean process in a unified GP framework. Predictive analytical equations are provided, integrating information shared across tasks through a relevant prior mean. This approach greatly improves the predictive performances, even far from observations, and may reduce significantly the computational complexity compared to traditional multi-task GP models. Our overall algorithm is called Magma (standing for Multi tAsk GPs with common MeAn). The quality of the mean process estimation, predictive performances, and comparisons to alternatives are assessed in various simulated scenarios and on real datasets.
Traditional multilevel model assumed independence between groups. Datasets are different from traditional hierarchical data when it is grouped by geographical units. The individual is influenced by not only its region...
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ISBN:
(纸本)9781479921867
Traditional multilevel model assumed independence between groups. Datasets are different from traditional hierarchical data when it is grouped by geographical units. The individual is influenced by not only its region but also the adjacent regions. It could include spatial dependence between groups. Therefore, it is necessary to build a new model and estimation method. In this paper, spatial statistics and spatial econometric models are introduced to random intercept model. Spatial dependence is reflected by spatial lag model in traditional level-2 model. Four types of parameters which include fixed effects, random level-1 coefficients, variance-covariance components, and spatial correlation error parameter need to estimate. Maximum likelihood estimation based on em algorithm and Fisher scoring algorithm for improved random intercept model is employed.
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