Computer Assisted Analysis of Mixtures and Applications
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Computer Assisted Analysis of Mixtures and Applications : Meta Analysis, Disease Mapping, and Others

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Description

Computer Assisted Analysis of Mixtures summarizes developments in the field over the last 20 years . Along with advancements in theory and algorithms, it explores developments in biometric applications, such as meta-analysis, disease mapping, fertility studies, estimation of prevalence under clustering, and estimation of the distribution of survival times under interval-censoring. The approach is nonparametric for the mixing distribution, including leaving the number of components of the mixing distribution unknown. The text is particularly valuable to statisticians working with pharmaceutical clinical trials, epidemiologists, and social scientists.
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Product details

  • Hardback | 248 pages
  • 158 x 228 x 18mm | 458.14g
  • Chapman & Hall/CRC
  • United States
  • English
  • 120 equations; 59 Tables, black and white
  • 1584881798
  • 9781584881797

Table of contents

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
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Review quote

"has several valuable features" Biometrics, Vol. 56, No. 2, June 2000 "The chapter on disease mapping is interesting and well illustrated" Biometrics, Vol. 56, No. 2, June 2000 "Overall, the book provides useful discussion of heterogeneity and algorithms." Biometrics, Vol. 56, No. 2, June 2000 "This software should permit the interested reader to carry out mixture analysis of their own data with little difficulty and facilitate a better appreciation of the methods presented." Short Book Reviews, Vol. 20, No. 3, December 2000 "The text is well written and easy to read." Short Book Reviews, Vol. 20, No. 3, December 2000
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