UID:
almafu_9960118460802883
Umfang:
1 online resource (xiv, 282 pages) :
,
digital, PDF file(s).
Ausgabe:
1st ed.
ISBN:
1-108-75991-2
,
1-108-75842-8
,
1-108-60457-9
Serie:
Institute of Mathematical Statistics textbooks ; 12
Inhalt:
This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.
Anmerkung:
Title from publisher's bibliographic system (viewed on 17 Jul 2019).
,
Cover -- Half-title -- Series information -- Title page -- Copyright information -- Dedication -- Contents -- Examples -- Preface -- 1 What Is an Exponential Family? -- 2 Examples of Exponential Families -- 2.1 Examples Important for the Sequel -- 2.2 Examples Less Important for the Sequel -- 2.3 Exercises -- 3 Regularity Conditions and Basic Properties -- 3.1 Regularity and Analytical Properties -- 3.2 Likelihood and Maximum Likelihood -- 3.3 Alternative Parameterizations -- 3.4 Solving Likelihood Equations Numerically: Newton-Raphson, Fisher Scoring and Other Algorithms -- 3.5 Conditional Inference for Canonical Parameter -- 3.6 Common Models as Examples -- 3.7 Completeness and Basu's Theorem -- 3.8 Mean Value Parameter and Cram[acute(e)]r-Rao (In)equality -- 4 Asymptotic Properties of the MLE -- 4.1 Large Sample Asymptotics -- 4.2 Small Sample Refinement: Saddlepoint Approximations -- 5 Testing Model-Reducing Hypotheses -- 5.1 Exact Tests -- 5.2 Fisher's Exact Test for Independence (or Homogeneity or Multiplicativity) in 2 [times] 2 Tables -- 5.3 Further Remarks on Statistical Tests -- 5.4 Large Sample Approximation of the Exact Test -- 5.5 Asymptotically Equivalent Large Sample Tests, Generally -- 5.6 A Poisson Trick for Deriving Large Sample Test Statistics in Multinomial and Related Cases -- 6 Boltzmann's Law in Statistics -- 6.1 Microcanonical Distributions -- 6.2 Boltzmann's Law -- 6.3 Hypothesis Tests in a Microcanonical Setting -- 6.4 Statistical Redundancy: An Information-Theoretic Measure of Model Fit -- 6.5 A Modelling Exercise in the Light of Boltzmann's Law -- 7 Curved Exponential Families -- 7.1 Introductory Examples -- 7.2 Basic Theory for ML Estimation and Hypothesis Testing -- 7.3 Statistical Curvature -- 7.4 More on Multiple Roots -- 7.5 Conditional Inference in Curved Families -- 8 Extension to Incomplete Data -- 8.1 Examples.
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8.2 Basic Properties -- 8.3 The EM Algorithm -- 8.4 Large-Sample Tests -- 8.5 Incomplete Data from Curved Families -- 8.6 Blood Groups under Hardy-Weinberg Equilibrium -- 8.8 Gaussian Factor Analysis Models -- 9 Generalized Linear Models -- 9.1 Basic Examples and Basic Definition -- 9.2 Likelihood Theory for Generalized Linear Models without Dispersion Parameter -- 9.3 Generalized Linear Models with Dispersion Parameter -- 9.4 Exponential Dispersion Models -- 9.5 Quasi-Likelihoods -- 9.6 GLMs versus Box-Cox Methodology -- 9.7 More Application Areas -- 10 Graphical Models for Conditional Independence Structures -- 10.1 Graphs for Conditional Independence -- 10.2 Graphical Gaussian Models -- 10.3 Graphical Models for Contingency Tables -- 10.4 Models for Mixed Discrete and Continuous Variates -- 11 Exponential Family Models for Graphs of Social Networks -- 11.1 Social Networks -- 11.2 The First Model Stage: Bernoulli Graphs -- 11.3 Markov Random Graphs -- 11.4 Illustrative Toy Example, n = 5 -- 11.5 Beyond Markov Models: General ERGM Type -- 12 Rasch Models for Item Response and Related Model Types -- 12.1 The Joint Model -- 12.2 The Conditional Model -- 12.3 Testing the Conditional Rasch Model Fit -- 12.4 Rasch Model Conditional Analysis by Log-Linear Models -- 12.5 Rasch Models for Polytomous Response -- 12.6 Factor Analysis Models for Binary Data -- 12.7 Models for Rank Data -- 13 Models for Processes in Space or Time -- 13.1 Models for Spatial Point Processes -- 13.2 Time Series Models -- 14 More Modelling Exercises -- 14.1 Genotypes under Hardy-Weinberg Equilibrium -- 14.2 Model for Controlled Multivariate Calibration -- 14.3 Refindings of Ringed Birds -- 14.4 Statistical Basis for Positron Emission Tomography -- Appendix A Statistical Concepts and Principles -- Appendix B Useful Mathematics -- B.1 Some Useful Matrix Results.
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B.2 Some Useful Calculus Results -- Bibliography -- Index.
Weitere Ausg.:
ISBN 1-108-47659-7
Sprache:
Englisch
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