Showing papers on "Mixture model published in 1988"

Mixture models : inference and applications to clustering

Abstract: General Introduction Introduction History of Mixture Models Background to the General Classification Problem Mixture Likelihood Approach to Clustering Identifiability Likelihood Estimation for Mixture Models via EM Algorithm Start Values for EMm Algorithm Properties of Likelihood Estimators for Mixture Models Information Matrix for Mixture Models Tests for the Number of Components in a Mixture Partial Classification of the Data Classification Likelihood Approach to Clustering Mixture Models with Normal Components Likelihood Estimation for a Mixture of Normal Distribution Normal Homoscedastic Components Asymptotic Relative Efficiency of the Mixture Likelihood Approach Expected and Observed Information Matrices Assessment of Normality for Component Distributions: Partially Classified Data Assessment of Typicality: Partially Classified Data Assessment of Normality and Typicality: Unclassified Data Robust Estimation for Mixture Models Applications of Mixture Models to Two-Way Data Sets Introduction Clustering of Hemophilia Data Outliers in Darwin's Data Clustering of Rare Events Latent Classes of Teaching Styles Estimation of Mixing Proportions Introduction Likelihood Estimation Discriminant Analysis Estimator Asymptotic Relative Efficiency of Discriminant Analysis Estimator Moment Estimators Minimum Distance Estimators Case Study Homogeneity of Mixing Proportions Assessing the Performance of the Mixture Likelihood Approach to Clustering Introduction Estimators of the Allocation Rates Bias Correction of the Estimated Allocation Rates Estimated Allocation Rates of Hemophilia Data Estimated Allocation Rates for Simulated Data Other Methods of Bias Corrections Bias Correction for Estimated Posterior Probabilities Partitioning of Treatment Means in ANOVA Introduction Clustering of Treatment Means by the Mixture Likelihood Approach Fitting of a Normal Mixture Model to a RCBD with Random Block Effects Some Other Methods of Partitioning Treatment Means Example 1 Example 2 Example 3 Example 4 Mixture Likelihood Approach to the Clustering of Three-Way Data Introduction Fitting a Normal Mixture Model to Three-Way Data Clustering of Soybean Data Multidimensional Scaling Approach to the Analysis of Soybean Data References Appendix

Families of Multivariate Distributions

Abstract: For many years there has been an interest in families of bivariate distributions with marginals as parameters. Genest and MacKay (1986a,b) showed that several such families that appear in the literature can be derived by a unified method. A similar conclusion is obtained in this article through the use of mixture models. These models might be regarded as multivariate proportional hazards models with random constants of proportionality. The mixture models are useful for two purposes. First, they make some properties of the derived distributions more transparent; the positive-dependency property of association is sometimes exposed, and a method for simulation of data from the distributions is suggested. But the mixture models also allow derivation of several new families of bivariate distributions with marginals as parameters, and they indicate obvious multivariate extensions. Some of the new families of bivariate distributions given in this article extend known distributions by adding a parameter ...

Monotonicity of quadratic-approximation algorithms

Abstract: It is desirable that a numerical maximization algorithm monotonically increase its objective function for the sake of its stability of convergence. It is here shown how one can adjust the Newton-Raphson procedure to attain monotonicity by the use of simple bounds on the curvature of the objective function. The fundamental tool in the analysis is the geometric insight one gains by interpreting quadratic-approximation algorithms as a form of area approximation. The statistical examples discussed include maximum likelihood estimation in mixture models, logistic regression and Cox's proportional hazards regression.

Fitting Mixture-Models to Grouped and Truncated Data Via the Em Algorithm

Abstract: The fitting of finite mixture models via the EM algorithm is considered for data which are available only in grouped form and which may also be truncated. A practical example is presented where a mixture of two doubly truncated log-normal distributions is adopted to model the distribution of the volume of red blood cells in cows during recovery from anemia.

Speech recognition using noise-adaptive prototypes

Abstract: A probabilistic mixture model is described for a frame (the short-term spectrum) of each to be used in speech recognition. Each component of the mixture is regarded as a prototype for the labeling phase of a hidden Markov model based speech recognition system. Since the ambient noise during recognition can differ from the ambient noise present in the training data, the model is designed for convenient updating in changing noise. Based on the observation that the energy in a frequency band is at any fixed time dominated either by signal energy or by noise energy, the authors model the energy as the larger of the separate energies of signal and noise in the band. Statistical algorithms are given for training this as a hidden variables model. The hidden variables are the prototype identities and the separate signal and noise components. A series of speech recognition experiments that successfully utilize this model is also discussed. >

The use of a mixture model in the analysis of count data.

Abstract: A mixture model is presented for the analysis of data on premature ventricular contractions. The analysis is shown to be straightforward and the conclusions relatively simple.

On the choice of starting values for the EM algorithm in fitting mixture models

Abstract: We consider the problem of finding suitable starting values for the EM algorithm in the fitting of finite mixture models to multivariate data. Given that the likelihood equation often has multiple roots for mixture models, the choice of starting values requires careful consideration. Attention is focussed here on the use of principal components to provide suitable starting values in this context. Examples are presented which involve the clustering of two real data sets.

A Bayesian approach to cluster analysis

Abstract: A general probabilistic model for describing the structure of statistical problems known under the generic name of cluster analysis, based on finite mixtures of distributions, is proposed. We analyse the theoretical and practical implications of this approach, and point out some open question on both the theoretical problem of determining the reference prior for models based on mixtures, and the practical problem of approximation that mixtures typically entail. Finally, models based on mixtures of normal distributions are analised with some detail