# FINITE MIXTURE MODELS MCLACHLAN PDF

View Table of Contents for Finite Mixture Models Geoffrey McLachlan · David Peel account of the theory and applications of modeling via finite mixture distributions. With an Summary · PDF · Request permissions · xml. By Geoffrey McLachlan and David Peel. Copyright DOWNLOAD PDF. Finite Finite Mixture and Markov Switching Models (Springer Series in Statistics). John Wiley, p. The importance of finite mixture models in the statistical analysis of data is underscored by the ever-increasing rate at which articles on.

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different cluster. In addition to clustering purposes, finite mixtures of distri- To this extent finite mixture models have continued to receive increasing attention from .. The reader is referred to McLachlan and Peel. () for a. Abstract: Finite mixture models are being increasingly used to model the distributions of a ization of the mixture probability density function (p.d.f.),. = (о ; y)м g. Request PDF on ResearchGate | On Jan 1, , Geoffrey J. McLachlan and others published Finite Mixture Model.

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High-breakdown linear discriminant analysis. Journal of the American Statistical Association — Google Scholar Huber P. Robust estimation of a location parameter. Annals of Mmathematical Statistics 73— Google Scholar Jolion J.

Robust clustering with applications in computer vision. Google Scholar Kent J. A curious likelihood identity for the multivariate t-distribution.

## Finite mixture models

Communications in Statistics — Simulation and Computation — Google Scholar Kharin Y. Robustness in Statistical Pattern Recognition. Kluwer, Dordrecht. Google Scholar Kosinski A. A procedure for the detection of multivariate outliers. Computational Statistics and Data Analysis — Google Scholar Kowalski J. On the rate of convergence of the ECME algorithm for multiple regression models with t-distributed errors.

Biometrika — Google Scholar Lange K. Robust statistical modeling using the t distribution.

## 1 Introduction

Google Scholar Lindsay B. Google Scholar Liu C. ML estimation of the multivariate t distribution and the EM algorithm. Journal of Multivariate Analysis — Statistica Sinica 5: 19— Google Scholar Markatou M. Mixture models, robustness and the weighted likelihood methodology. Technical Report No.

Department of Statistics, Stanford University, Stanford. Weighted likelihood equations with bootstrap root search. Google Scholar McLachlan G. Mixture Models: Inference and Applications to Clustering.

Marcel Dekker, New York. Robust cluster analysis via mixtures of multivariate t-distributions. In: Amin A.

Springer-Verlag, Berlin, pp. Fitting of mixtures of normal and t-components.

## EM Estimation for Finite Mixture Models with Known Mixture Component Size

Journal of Statistical Software 4 2. Google Scholar Meng X. The EM algorithm — an old folk song sung to a fast new tune with discussion.

Google Scholar Rocke D. Robust estimation of multivariate location and shape. Journal of Statistical Planning and Inference — Google Scholar Rousseeuw P.

Fuzzy clustering using scatter matrices. Google Scholar Rubin D. Iteratively reweighted least squares. Abstract We consider the use of an EM algorithm for fitting finite mixture models when mixture component size is known. This situation can occur in a number of settings, where individual membership is unknown but aggregate membership is known.

When the mixture component size, i.

## McLachlan G., Peel D. Finite Mixture Models

This approach does not, however, entirely account for the fact that the number of observations within each mixture component is known, which may result in artificially incorrect estimates of parameters.

By fully capitalizing on the available information, the proposed EM algorithm shows robustness to the choice of starting values and exhibits numerically stable convergence properties.

Keywords: Aggregate data, Conditional Bernoulli distribution, EM algorithm, Finite mixture models 1 Introduction Finite mixture models have been powerful tools for analyzing data where observations originate from various components but the component membership of each observation is not known.

The analysis of such finite mixture models is commonly carried out using maximum likelihood estimation with the EM algorithm Dempster et al. The finite mixture model has been extended to data with known mixture component size, i.

The computational difficulty of fitting such a finite mixture model with known mixture component size, however, has hindered correct EM estimation and given rise to inconsistent EM estimates depending on starting values Nettleton, ; Friede and Kieser, Here we focus on the problem of fitting a two-component mixture model with known mixture component size.

The finite mixture problems with more than two mixture components would be solved by a nontrivial generalization of the method proposed in this paper.

Our work was specifically motivated by sample size adaptive designs for clinical trials. We want to consider adaptive designs that allow the estimation of nuisance parameters at an interim stage of a trial without breaking the blind for treatment identity.

To deal with known treatment group size, their EM algorithm fixed the mixing probability parameter at the proportion of patients assigned to the experimental group.

By doing so, the EM algorithm devised by Gould and Shih sometimes produced an incorrect estimate toward the boundary of the parameter space Nettleton, In clinical trials, it is also common practice to randomize patients to treatments using randomly permuted blocks Rosenberger and Lachin, Statistical Predication Analysis.

Finite mixture distributions.

Here we focus on the problem of fitting a two-component mixture model with known mixture component size. Google Scholar Meng X. Fitting Mixture Models to Binned Data.

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