Computer Assisted Analysis of Mixtures and Applications

1. Auflage 1999
ISBN: 978-1-58488-179-7
Verlag: Chapman and Hall/CRC

Buch, Englisch, Band 81, 248 Seiten, Format (B × H): 161 mm x 238 mm, Gewicht: 462 g

Reihe: Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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.

Zielgruppe

AudienceMedical andPharmacological StatisticiansEpidemiologistsSocial Scientists

Autoren/Hrsg.

Bohning, Dankmar

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

INTRODUCTIONPopulation Heterogeneity: the Natural Genesis of Mixture ModelsSome ExamplesClassification Using Posterior BayesParametric or Nonparametric Mixture ModelsConnection to Empirical Bayes EstimationTHEORY OF NONPARAMETRIC MIXTURE MODELSThe Likelihood and its PropertiesThe Directional Derivative and the Gradient FunctionThe General Mixture Maximum Likelihood TheoremApplications of the TheoremALGORITHMSVertex Direction MethodVertex Exchange MethodStep-Length ChoicesC.A. MANThe EM Algorithm for the Fixed Component CaseTHE LIKELIHOOD RATIO TEST FOR THE NUMBER OF COMPONENTSThe ProblemSome Analytical SolutionsSimulation and Bootstrap SolutionsC.A.MAN-APPLICATION: META-ANALYSISConventional ApproachHeterogeneityC.A.MAN Solution for Modeling HeterogeneityClassification of Studies Using Posterior BayesMOMENT ESTIMATORS OF THE VARIANCE OF MIXING DISTRIBUTIONThe DerSimonian-Laird EstimatorThe Bohning-Sarol EstimatorEstimation of Binomia- or Poisson Rate Under HeterogeneityC.A. MAN-APPLICATION: DISEASE MAPPINGConventional Approach I: Mapping PercentilesConventional Approach II: Mapping P-ValuesEstimating Map HeterogeneityOTHER C.A. MAN APPLICATIONSFertility StudiesModeling the Diagnostic SituationInterval-Censored Survival Data