Computer Assisted Analysis of Mixtures and Applications

INTRODUCTION
Population Heterogeneity: the Natural Genesis of Mixture Models
Some Examples
Classification Using Posterior Bayes
Parametric or Nonparametric Mixture Models
Connection to Empirical Bayes Estimation
THEORY OF NONPARAMETRIC MIXTURE MODELS
The Likelihood and its Properties
The Directional Derivative and the Gradient Function
The General Mixture Maximum Likelihood Theorem
Applications of the Theorem
ALGORITHMS
Vertex Direction Method
Vertex Exchange Method
Step-Length Choices
C.A. MAN
The EM Algorithm for the Fixed Component Case
THE LIKELIHOOD RATIO TEST FOR THE NUMBER OF COMPONENTS
The Problem
Some Analytical Solutions
Simulation and Bootstrap Solutions
C.A.MAN-APPLICATION: META-ANALYSIS
Conventional Approach
Heterogeneity
C.A.MAN Solution for Modeling Heterogeneity
Classification of Studies Using Posterior Bayes
MOMENT ESTIMATORS OF THE VARIANCE OF MIXING DISTRIBUTION
The DerSimonian-Laird Estimator
The Bohning-Sarol Estimator
Estimation of Binomia- or Poisson Rate Under Heterogeneity
C.A. MAN-APPLICATION: DISEASE MAPPING
Conventional Approach I: Mapping Percentiles
Conventional Approach II: Mapping P-Values
Estimating Map Heterogeneity
OTHER C.A. MAN APPLICATIONS
Fertility Studies
Modeling the Diagnostic Situation
Interval-Censored Survival Data