عنوان

Statistical modelling by exponential families /

1108604579

9781108604574

1108476597

1108701116

9781108476591

9781108701112

Statistical modelling by exponential families /

[Book]

Rolf Sundberg.

Cambridge :

Cambridge University Press,

2019.

1 online resource (xiv, 282 pages) :

illustrations

Institute of Mathematical Statistics textbooks ;

12

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

10 Graphical Models for Conditional Independence Structures10.1 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

3.6 Common Models as Examples3.7 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 Cases6 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 Data8.1 Examples; 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

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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-Lf̲ 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.

9781108476591

Distribution (Probability theory), Problems, exercises, etc.

Exponential families (Statistics), Problems, exercises, etc.

Distribution (Probability theory)

Exponential families (Statistics)

Sundberg, Rolf,1942-

20200822151318.0

pn

[Book]

Y