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12th IEEE International Conference on Signal Processing (ICSP)

作者： Min Suqin Commun Univ China Sch Sci Beijing Peoples R China

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.

关键词： Random intercept model autocorrelation EM algorithm fisher scoring algorithm

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Efficient estimation for incomplete multivariate data

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2012年第5期142卷 1215-1224页

作者： Jorgensen, Bent Petersen, Hans Chr. Univ So Denmark Dept Math & Comp Sci DK-5230 Odense M Denmark

We review the fisher scoring and EM algorithms for incomplete multivariate data from an estimating function point of view, and examine the corresponding quasi-score functions under second-moment assumptions. A bias-corrected REML-type estimator for the covariance matrix is derived, and the fisher, Godambe and empirical sandwich information matrices are compared. We make a numerical investigation of the two algorithms, and compare with a hybrid algorithm, where fisher scoring is used for the mean vector and the EM algorithm for the covariance matrix. (C) 2011 Elsevier B.V. All rights reserved.

关键词： EM algorithm Estimating function fisher scoring algorithm Godambe information matrix Missing data REML estimation

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Heteroscedastic normal-exponential mixture models: Bayesian and classical approaches

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APPLIED MATHEMATICS AND COMPUTATION 2011年第7期218卷 3635-3648页

作者： Garrido Lopera, Liliana Cepeda-Cuervo, Edilberto Achcar, Jorge Alberto Univ Nacl Colombia Dept Estadist Bogota Colombia Univ Los Andes Dept Math Bogota Colombia Univ Sao Paulo FMRP Dept Social Med BR-05508 Sao Paulo Brazil

In this paper, we introduce a Bayesian analysis for mixture of distributions belonging to the exponential family. As a special case we consider a mixture of normal exponential distributions including joint modeling of the mean and variance. We also consider joint modeling of the mean and variance heterogeneity. Markov Chain Monte Carlo (MCMC) methods are used to obtain the posterior summaries of interest. We also introduce and apply an EM algorithm, where the maximization is obtained applying the fisher scoring algorithm. Finally, we also include analysis of real data sets to illustrate the proposed methodology. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Mixture models Variance heterogeneity Bayesian methods MCMC simulation Classical approach EM algorithm fisher scoring algorithm

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An improved method for the computation of maximum likeliood estimates for multinomial overdispersion models

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2005年第1期49卷 33-43页

作者： Neerchal, NK Morel, JG Univ Maryland Baltimore Cty Dept Math & Stat Baltimore MD 21250 USA P&G Pharmaceut Inc Biometr & Stat Sci Dept Mason OH 45040 USA

In this article, we consider the maximum likelihood estimation of two commonly used overdispersion models, namely, the Dirichlet-multinomial distribution (DM), due to Mosimann (Biometrika 49 (1962) 65), and a finite mixture distribution (FM) proposed by Morel and Nagaraj (Biometrika 80 (1993) 363), and Neerchal and Morel (J. Amer. Statist. Assoc. 93 (1998) 1078). These models have been successfully used in the literature for modeling overdispersion in multinomial data. Maximum likelihood estimation of the parameters of these models using the classical fisher scoring method poses certain computational challenges. In the case of DM, the challenges are overcome by noting that the fisher information matrix can be computed using the beta-binomial distribution (BB), which is the univariate version of DIM. On the other hand, in the case of FM, an approximation theorem call be used to obtain a two-stage procedure for computing the maximum likelihood estimates. Simulation results show that the two-stage procedure is faster without loosing any accuracy. (C) 2004 Elsevier B.V. All rights reserved.

关键词： mixture of multinomial distributions fisher scoring algorithm Dirichlet-multinomial distribution beta-binomial distribution

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Analysis of computer experiments using penalized likelihood in Gaussian kriging models

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TECHNOMETRICS 2005年第2期47卷 111-120页

作者： Li, RZ Sudjianto, A Penn State Univ Dept Stat University Pk PA 16802 USA Bank Amer Risk Management Qual & Prod Charlotte NC 28255 USA

Kriging is a popular analysis approach for computer experiments for the purpose of creating a cheap-to-compute "meta-model" as a surrogate to a computationally expensive engineering simulation model. The maximum likelihood approach is used to estimate the parameters in the kriging model. However, the likelihood function near the optimum may be flat in some situations, which leads to maximum likelihood estimates for the parameters in the covariance matrix that have very large variance. To overcome this difficulty, a penalized likelihood approach is proposed for the kriging model. Both theoretical analysis and empirical experience using real world data suggest that the proposed method is particularly important in the context of a computationally intensive simulation model where the number of simulation runs must be kept small because collection of a large sample set is prohibitive. The proposed approach is applied to the reduction of piston slap, an unwanted engine noise due to piston secondary motion. Issues related to practical implementation of the proposed approach are discussed.

关键词： computer experiment fisher scoring algorithm kriging meta-model penalized likelihood smoothly clipped absolute deviation

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Statistical modelling of artificial neural networks using the multi-layer perceptron

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STATISTICS AND COMPUTING 2003年第3期13卷 227-239页

作者： Aitkin, M Foxall, R Newcastle Univ Dept Stat Newcastle Upon Tyne NE1 7RU Tyne & Wear England

Multi-layer perceptrons (MLPs), a common type of artificial neural networks (ANNs), are widely used in computer science and engineering for object recognition, discrimination and classification, and have more recently found use in process monitoring and control. "Training" such networks is not a straightforward optimisation problem, and we examine features of these networks which contribute to the optimisation difficulty. Although the original "perceptron", developed in the late 1950s (Rosenblatt 1958, Widrow and Hoff 1960), had a binary output from each "node", this was not compatible with back-propagation and similar training methods for the MLP. Hence the output of each node (and the final network output) was made a differentiable function of the network inputs. We reformulate the MLP model with the original perceptron in mind so that each node in the "hidden layers" can be considered as a latent (that is, unobserved) Bernoulli random variable. This maintains the property of binary output from the nodes, and with an imposed logistic regression of the hidden layer nodes on the inputs, the expected output of our model is identical to the MLP output with a logistic sigmoid activation function (for the case of one hidden layer). We examine the usual MLP objective function-the sum of squares-and showits multi-modal form and the corresponding optimisation difficulty. We also construct the likelihood for the reformulated latent variable model and maximise it by standard finite mixture ML methods using an EM algorithm, which provides stable ML estimates from random starting positions without the need for regularisation or cross-validation. Over-fitting of the number of nodes does not affect this stability. This algorithm is closely related to the EM algorithm of Jordan and Jacobs (1994) for the Mixture of Experts model. We conclude with some general comments on the relation between the MLP and latent variable models.

关键词： artificial neural network multi-layer perceptron hierarchical mixture of experts EM algorithm fisher scoring algorithm

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Analysis of capture-recapture data with a Rasch-type model allowing for conditional dependence and multidimensionality

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BIOMETRICS 2001年第3期57卷 714-719页

作者： Bartolucci, F Forcina, A Univ Perugia Dipartimento Sci Stat I-06100 Perugia Italy

In this article, we show that, if subjects are assumed to be homogeneous within it finite set of latent classes, the basic restrictions of the Rasch model (conditional independence and unidimensionality) can be relaxed in a flexible way by simply adding appropriate columns to a basic design matrix. When discrete covariates are available so that subjects may be classified into strata, we show how a joint modeling approach can achieve greater parsimony. Parameter estimates may be obtained by maximizing the conditional likelihood (given the total number of captures) with a combined use of the EM and fisher scoring algorithms. We also discuss a technique for obtaining confidence intervals for the size of the population under study based on the profile likelihood.

关键词： EM algorithm fisher scoring algorithm latent class models marginal modeling profile likelihood

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Simple fitting algorithms for incomplete categorical data

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL 1997年第2期59卷 401-414页

作者： Molenberghs, G Goetghebeur, E Limburgs Universitair Centrum Universitair Campus B-3590 Diepenbeek BE [*] G. Molenberghs Biostatistics Limburgs Universitair Centrum Universitair Campus B-3590 Diepenbeek Belgium. gmolenb@luc.ac.be

A popular approach to estimation based on incomplete data is the EM algorithm. For categorical data, this paper presents a simple expression of the observed data log-likelihood and its derivatives in terms of the complete data for a broad class of models and missing data patterns. We show that using the observed data likelihood directly is easy and has some advantages. One can gain considerable computational speed over the EM algorithm and a straightforward variance estimator is obtained for the parameter estimates. The general formulation treats a wide range of missing data problems in a uniform way. Two examples are worked out in full.

关键词： coarsened data EM algorithm fisher scoring algorithm generalized linear models longitudinal data maximum likelihood estimation missing values multivariate categorical data repeated measures

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Methods for analyzing multivariate binary data, with association between outcomes of interest

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BIOMETRICS 1996年第3期52卷 1121-1133页

作者： Molenberghs, G Ritter, LL INT INST DRUG DEV B-1050 BRUSSELSBELGIUM

A likelihood based method is proposed for multivariate categorical data. It is assumed that, together with the marginal outcomes, the set of pairwise associations between outcomes is of scientific interest. The focus is on binary outcomes and it is indicated how the proposed method generalizes to categorical outcomes. A connection with second-order generalized estimating equations (GEE2) is established. The method is applied to analyze data from a developmental toxicity study.

关键词： binary data categorical data fisher scoring algorithm generalized estimating equations likelihood function maximum likelihood estimation odds ratio

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FACTOR-ANALYSIS FOR CLUSTERED OBSERVATIONS

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PSYCHOMETRIKA 1992年第4期57卷 581-597页

作者： LONGFORD, NT MUTHEN, BO UNIV CALIF LOS ANGELES LOS ANGELESCA 90024

Classical factor analysis assumes a random sample of vectors of observations. For clustered vectors of observations, such as data for students from colleges, or individuals within households, it may be necessary to consider different within-group and between-group factor structures. Such a two-level model for factor analysis is defined, and formulas for a scoring algorithm for estimation with this model are derived. A simple noniterative method based on a decomposition of the total sums of squares and crossproducts is discussed. This method provides a suitable starting solution for the iterative algorithm, but it is also a very good approximation to the maximum likelihood solution. Extensions for higher levels of nesting are indicated. With judicious application of quasi-Newton methods, the amount of computation involved in the scoring algorithm is moderate even for complex problems;in particular, no inversion of matrices with large dimensions is involved. The methods are illustrated on two examples.

关键词： FACTOR ANALYSIS fisher scoring algorithm MAXIMUM LIKELIHOOD MULTILEVEL ANALYSIS

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