Computer Assisted Analysis of Mixtures and Applications

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

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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 more

Product details

  • Hardback | 248 pages
  • 158 x 228 x 18mm | 458.14g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • United States
  • English
  • 59 black & white tables
  • 1584881798
  • 9781584881797

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 2000show more

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 Datashow more