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Statistical Modelling by Exponential Families [Hardback]

(Stockholms Universitet)
  • Formāts: Hardback, 296 pages, height x width x depth: 235x157x20 mm, weight: 560 g, Worked examples or Exercises; 22 Line drawings, black and white
  • Sērija : Institute of Mathematical Statistics Textbooks
  • Izdošanas datums: 29-Aug-2019
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1108476597
  • ISBN-13: 9781108476591
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  • Cena: 150,95 €
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Statistical Modelling by Exponential FamiliesPalielināt
  • Formāts: Hardback, 296 pages, height x width x depth: 235x157x20 mm, weight: 560 g, Worked examples or Exercises; 22 Line drawings, black and white
  • Sērija : Institute of Mathematical Statistics Textbooks
  • Izdošanas datums: 29-Aug-2019
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1108476597
  • ISBN-13: 9781108476591
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781108476591.html
Keywords:
This readable, digestible introduction to exponential families of distributions covers the essential theory and demonstrates its use in applications. Containing a vast set of examples and numerous exercises, it is written for graduate students and researchers with a background in basic statistical inference.

Recenzijas

'Rolf Sundberg's book gives attractive properties of the exponential family and illustrates them for a wide variety of applications. Definitions are concise and most propositions look directly appealing. The writing reflects the author's experience in deriving results that are essential for good modelling and convincing inference. Thus, this book is indispensable for all data scientists, be they graduate students or experienced researchers.' Nanny Wermuth, Chalmers tekniska högskola, Sweden 'This is an excellent book on exponential families. It covers not only the basic properties of exponential families but also several modern topics such as graphical models and random networks. The author blends theories and applications elegantly and provides several useful examples from various scientific domains. It is suitable for a one-semester graduate-level course and will be an excellent reference for topic courses such as stochastic modeling and parametric models.' Yen-Chi Chen, Journal of the American Statistical Association 'Overall, this is a clearly written, graduate-level introduction to an important area of statistical modelling. The numerous examples and exercises included throughout provide invaluable illustrations across a number of application areas, making this a useful reference for both researchers and practitioners. As a textbook, it is an excellent starting point for either a taught course on statistical inference with an emphasis on data from the exponential family, or for self-directed study in this area.' Fraser Daly, Institute of Mathematical Statistics Textbooks 'This book is perfect for an introductory theoretical graduate course but its parts could also definitely be used in a more applied course. The only prerequisite is basic mathematical statistics. The book is also very handy as a general reference on exponential families. To keep the content simple, the author sometimes avoids the most technical details; however, all necessary references are provided for the reader's convenience. In this sense the book can be used by any researcher interested in exponential families from either a more theoretical or more applied point of view.' Piotr Zwiernik, MathSciNet

Papildus informācija

A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.
Examples ix
Preface xii
1 What Is an Exponential Family?
1(5)
2 Examples of Exponential Families
6(18)
2.1 Examples Important for the Sequel
6(9)
2.2 Examples Less Important for the Sequel
15(6)
2.3 Exercises
21(3)
3 Regularity Conditions and Basic Properties
24(40)
3.1 Regularity and Analytical Properties
24(7)
3.2 Likelihood and Maximum Likelihood
31(5)
3.3 Alternative Parameterizations
36(9)
3.4 Solving Likelihood Equations Numerically
45(1)
3.5 Conditional Inference for Canonical Parameter
46(4)
3.6 Common Models as Examples
50(9)
3.7 Completeness and Basu's Theorem
59(2)
3.8 Mean Value Parameter and Cramer--Rao (In)equality
61(3)
4 Asymptotic Properties of the MLE
64(11)
4.1 Large Sample Asymptotics
64(6)
4.2 Small Sample Refinement: Saddlepoint Approximations
70(5)
5 Testing Model-Reducing Hypotheses
75(25)
5.1 Exact Tests
76(4)
5.2 Fisher's Exact Test for Independence, Homogeneity, Etc.
80(4)
5.3 Further Remarks on Statistical Tests
84(2)
5.4 Large Sample Approximation of the Exact Test
86(4)
5.5 Asymptotically Equivalent Large Sample Tests
90(4)
5.6 A Poisson Trick for Deriving Test Statistics
94(6)
6 Boltzmann's Law in Statistics
100(18)
6.1 Microcanonical Distributions
100(2)
6.2 Boltzmann's Law
102(6)
6.3 Hypothesis Tests in a Microcanonical Setting
108(1)
6.4 Statistical Reduncancy
109(5)
6.5 A Modelling Exercise in the Light of Boltzmann's Law
114(4)
7 Curved Exponential Families
118(25)
7.1 Introductory Examples
118(6)
7.2 Basic Theory for ML Estimation and Hypothesis Testing
124(5)
7.3 Statistical Curvature
129(2)
7.4 More on Multiple Roots
131(5)
7.5 Conditional Inference in Curved Families
136(7)
8 Extension to Incomplete Data
143(21)
8.1 Examples
143(4)
8.2 Basic Properties
147(3)
8.3 The EM Algorithm
150(5)
8.4 Large-Sample Tests
155(1)
8.5 Incomplete Data from Curved Families
155(1)
8.6 Blood Groups under Hardy--Weinberg Equilibrium
156(3)
8.7 Hidden Markov Models
159(2)
8.8 Gaussian Factor Analysis Models
161(3)
9 Generalized Linear Models
164(27)
9.1 Basic Examples and Basic Definition
164(5)
9.2 Models without Dispersion Parameter
169(6)
9.3 Models with Dispersion Parameter
175(6)
9.4 Exponential Dispersion Models
181(2)
9.5 Quasi-Likelihoods
183(1)
9.6 GLMs versus Box--Cox Methodology
184(2)
9.7 More Application Areas
186(5)
10 Graphical Models for Conditional Independence Structures
191(19)
10.1 Graphs for Conditional Independence
192(3)
10.2 Graphical Gaussian Models
195(6)
10.3 Graphical Models for Contingency Tables
201(4)
10.4 Models for Mixed Discrete and Continuous Variates
205(5)
11 Exponential Family Models for Social Networks
210(18)
11.1 Social Networks
210(1)
11.2 The First Model Stage: Bernoulli Graphs
211(1)
11.3 Markov Random Graphs
212(6)
11.4 Illustrative Toy Example, n = 5
218(7)
11.5 Beyond Markov Models: General ERGM Type
225(3)
12 Rasch Models for Item Response and Related Models
228(18)
12.1 The Joint Model
229(2)
12.2 The Conditional Model
231(3)
12.3 Testing the Conditional Rasch Model Fit
234(5)
12.4 Rasch Model Conditional Analysis by Log-Linear Models
239(1)
12.5 Rasch Models for Polytomous Response
240(1)
12.6 Factor Analysis Models for Binary Data
241(2)
12.7 Models for Rank Data
243(3)
13 Models for Processes in Space or Time
246(12)
13.1 Models for Spatial Point Processes
246(8)
13.2 Time Series Models
254(4)
14 More Modelling Exercises
258(7)
14.1 Genotypes under Hardy-Weinberg Equilibrium
258(1)
14.2 Model for Controlled Multivariate Calibration
259(1)
14.3 Refindings of Ringed Birds
259(3)
14.4 Statistical Basis for Positron Emission Tomography
262(3)
Appendix A Statistical Concepts and Principles
265(3)
Appendix B Useful Mathematics
268(3)
B.1 Some Useful Matrix Results
268(1)
B.2 Some Useful Calculus Results
269(2)
Bibliography 271(7)
Index 278
Rolf Sundberg is Professor Emeritus of Statistical Science at Stockholms Universitet. His work embraces both theoretical and applied statistics, including principles of statistics, exponential families, regression, chemometrics, stereology, survey sampling inference, molecular biology, and paleoclimatology. In 2003, with M. Linder, he won the award for best theoretical paper in the Journal of Chemometrics for their work on multivariate calibration, and in 2017 he was named Statistician of the Year by the Swedish Statistical Society.