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El. knyga: Frontiers of Statistical Decision Making and Bayesian Analysis: In Honor of James O. Berger

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  • Formatas: PDF+DRM
  • Išleidimo metai: 24-Jul-2010
  • Leidėjas: Springer-Verlag New York Inc.
  • Kalba: eng
  • ISBN-13: 9781441969446
Kitos knygos pagal šią temą:
Frontiers of Statistical Decision Making and Bayesian Analysis: In Honor of James O. BergerDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Išleidimo metai: 24-Jul-2010
  • Leidėjas: Springer-Verlag New York Inc.
  • Kalba: eng
  • ISBN-13: 9781441969446
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Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis, and posterior simulation methods.

Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance, and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

Recenzijos

From the reviews:

The book is a Festschrift in honour of Jim Bergers 60th birthday that was celebrated at a conference in spring 2010 in Texas. All the papers are written by experts in their fields and represent the current state of the art in Bayesian modelling. for those who are interested in Bayesian modelling, there are some interesting aspects to be detected. the book is aimed for advanced researchers in Bayesian analyses. (Wolfgang Polasek, International Statistical Review, Vol. 79 (3), 2011)

This collection contains invited papers by statisticians to honor and acknowledge the contributions of James O. Berger to Bayesian statistics. These papers present recent surveys and developments within the area of statistical decision theory and Bayesian statistics and related topics. Each chapter provides a detailed treatment of the topic under consideration. can be useful for graduate students and researchers from diverse fields of statistics and related disciplines. this edited volume contains a wealth of knowledge, wisdom and information on Bayesian statistics. (Technometrics, Vol. 53 (2), May, 2011)

1 Introduction
1(30)
1.1 Biography of James O. Berger
1(1)
1.2 The Frontiers of Research at SAMSI
2(25)
1.2.1 Research Topics from Past SAMSI Programs
3(19)
1.2.2 Research Topics from Current SAMSI Programs
22(2)
1.2.3 Research Topics in Future Programs
24(3)
1.3 Overview of the Book
27(4)
2 Objective Bayesian Inference with Applications
31(38)
2.1 Bayesian Reference Analysis of the Hardy-Weinberg Equilibrium
31(13)
Jose M. Bernardo
Vera Tomazella
2.1.1 Problem Statement
32(1)
2.1.2 Objective Precise Bayesian Testing
33(2)
2.1.3 Testing for Hardy-Weinberg Equilibrium
35(6)
2.1.4 Examples
41(3)
2.2 Approximate Reference Priors in the Presence of Latent Structure
44(12)
Brunero Liseo
Andrea Tancredi
Maria M. Barbieri
2.2.1 The Method
45(2)
2.2.2 Examples
47(6)
2.2.3 The Case with Nuisance Parameters
53(2)
2.2.4 Conclusions
55(1)
2.3 Reference Priors for Empirical Likelihoods
56(13)
Bertrand Clarke
Ao Yuan
2.3.1 Empirical Likelihood
57(1)
2.3.2 Reference Priors
58(3)
2.3.3 Relative Entropy Reference Priors
61(4)
2.3.4 Hellinger Reference Prior
65(1)
2.3.5 Chi-square Reference Prior
66(2)
2.3.6 Discussion
68(1)
3 Bayesian Decision Based Estimation and Predictive Inference
69(44)
3.1 Bayesian Shrinkage Estimation
69(14)
William E. Strawderman
3.1.1 Some Intuition into Shrinkage Estimation
70(2)
3.1.2 Some Theory for the Normal Case with Covariance σ2I
72(5)
3.1.3 Results for Known Σ and General Quadratic Loss
77(5)
3.1.4 Conclusion and Extensions
82(1)
3.2 Bayesian Predictive Density Estimation
83(12)
Edward I. George
Xinyi Xu
3.2.1 Prediction for the Multivariate Normal Distribution
85(3)
3.2.2 Predictive Density Estimation for Linear Regression
88(2)
3.2.3 Multiple Shrinkage Predictive Density Estimation
90(1)
3.2.4 Simulation Studies
91(4)
3.2.5 Concluding Remarks
95(1)
3.3 Automated Bias-variance Trade-off: Intuitive Inadmissibility or Inadmissible Intuition?
95(18)
Xiao-Li Meng
3.3.1 Always a Good Question
96(1)
3.3.2 Gene-Environment Interaction and a Misguided Insight
97(3)
3.3.3 Understanding Partially Bayes Methods
100(3)
3.3.4 Completing M&C's Argument
103(2)
3.3.5 Learning through Exam: The Actual Qualifying Exam Problem
105(2)
3.3.6 Interweaving Research and Pedagogy: The Actual Annotated Solution
107(4)
3.3.7 A Piece of Inadmissible Cake?
111(2)
4 Bayesian Model Selection and Hypothesis Tests
113(44)
4.1 Performance of Bayesian Model Selection Criteria for Gaussian Mixture Models
113(17)
Russell J. Steele
Adrian E. Raftery
4.1.1 Bayesian Model Selection for Mixture Models
114(4)
4.1.2 A Unit Information Prior for Mixture Models
118(4)
4.1.3 Examples
122(3)
4.1.4 Simulation Study
125(4)
4.1.5 Discussion
129(1)
4.2 How Large Should the Training Sample Be?
130(12)
Luis Pericchi
4.2.1 General Methodology
131(4)
4.2.2 An Exact Calculation
135(7)
4.2.3 Discussion of the FivePercent-Cubic-Root Rule
142(1)
4.3 A Conservative Property of Bayesian Hypothesis Tests
142(4)
Valen E. Johnson
4.3.1 An Inequality
143(2)
4.3.2 Discussion
145(1)
4.4 An Assessment of the Performance of Bayesian Model Averaging in the Linear Model
146(11)
Ilya Lipkovich
Keying Ye
Eric P. Smith
4.4.1 Assessment of BMA Performance
148(1)
4.4.2 A Simulation Study of BMA Performance
149(6)
4.4.3 Summary
155(2)
5 Bayesian Inference for Complex Computer Models
157(28)
5.1 A Methodological Review of Computer Models
157(11)
M.J. Bayarri
5.1.1 Computer Models and Emulators
158(1)
5.1.2 The Discrepancy (Bias) Function
159(4)
5.1.3 Confounding of Tuning and Bias
163(1)
5.1.4 Modularization
164(3)
5.1.5 Additional Issues
167(1)
5.1.6 Summary
168(1)
5.2 Computer Model Calibration with Multivariate Spatial Output
168(17)
K. Sham Bhat
Murali Haran
Marlos Goes
5.2.1 Computer Model Calibration with Spatial Output
170(2)
5.2.2 Calibration with Multivariate Spatial Output
172(4)
5.2.3 Application to Climate Parameter Inference
176(3)
5.2.4 Results
179(5)
5.2.5 Summary
184(1)
6 Bayesian Nonparametrics and Semi-parametrics
185(34)
6.1 Bayesian Nonparametric Goodness of Fit Tests
185(9)
Surya T. Tokdar
Arijit Chakrabarti
Jayanta K. Ghosh
6.1.1 An Early Application of Bayesian Ideas in Goodness of Fit Problems
187(1)
6.1.2 Testing a Point Null versus Non-parametric Alternatives
187(2)
6.1.3 Posterior Consistency for a Composite Goodness of Fit Test
189(3)
6.1.4 Bayesian Goodness of Fit Tests
192(2)
6.2 Species Sampling Model and Its Application to Bayesian Statistics
194(13)
Jaeyong Lee
6.2.1 Basic Theory
196(5)
6.2.2 Construction Methods for EPPFs
201(3)
6.2.3 Statistical Applications
204(2)
6.2.4 Discussion
206(1)
6.3 Hierarchical Models, Nested Models, and Completely Random Measures
207(12)
Michael I. Jordan
6.3.1 Completely Random Measures
208(2)
6.3.2 Marginal Probabilities
210(2)
6.3.3 Hierarchical Models
212(2)
6.3.4 Nested Models
214(2)
6.3.5 Discussion
216(3)
7 Bayesian Influence and Frequentist Interface
219(38)
7.1 Bayesian Influence Methods
219(18)
Hongtu Zhu
Joseph G. Ibrahim
Hyunsoon Cho
Niansheng Tang
7.1.1 Bayesian Case Influence Measures
221(5)
7.1.2 Bayesian Global and Local Robustness
226(7)
7.1.3 An Illustrative Example
233(4)
7.2 The Choice Of Nonsubjeclive Priors on Hyperparametcrs for Hierarchical Bayes Models
237(10)
Gauri S. Datta
J.N.K. Rao
7.2.1 Probability Matching in Small Area Estimation
240(2)
7.2.2 Frequentist Evaluation of Posterior Variance
242(3)
7.2.3 Discussion
245(2)
7.3 Exact Matching Inference for a Multivariale Normal Model
247(10)
Luyan Dai
Dongchu Sun
7.3.1 The Background
249(3)
7.3.2 Main Results
252(5)
8 Bayesian Clinical Trials
257(28)
8.1 Application of a Bayesian Doubly Optimal Group Sequential Design for Clinical Trials
257(13)
J. Kyle Wathen
Peter F. Thall
8.1.1 A Non-Small Cell Lung Cancer Trial
257(2)
8.1.2 Bayesian Doubly Optimal Group Sequential Designs
259(3)
8.1.3 Application of BDOGS to the Lung Cancer Trial
262(7)
8.1.4 Discussion
269(1)
8.2 Experimental Design and Sample Size Computations for Longitudinal Models
270(7)
Robert E. Weiss
Yan Wang
8.2.1 Covariates and Missing Data
271(1)
8.2.2 Simulating the Predictive Distributions of the Bayes Factor
271(1)
8.2.3 Sample Size for a New Repeated Measures Pediatric Pain Study
272(5)
8.3 A Bayes Rule for Subgroup Reporting
277(8)
Peter Muller
Siva Sivaganesan
Purushottam W. Laud
8.3.1 The Model Space
277(1)
8.3.2 Subgroup Selection as a Decision Problem
278(3)
8.3.3 Probability Model
281(1)
8.3.4 A Dementia Trial
282(2)
8.3.5 Discussion
284(1)
9 Bayesian Methods for Genomics, Molecular and Systems Biology
285(42)
9.1 Bayesian Modelling for Biological Annotation of Gene Expression Pathway Signatures
285(18)
Haige Shen
Mike West
9.1.1 Context and Models
287(3)
9.1.2 Computation
290(3)
9.1.3 Evaluation and Illustrations
293(3)
9.1.4 Applications to Hormonal Pathways in Breast Cancer
296(4)
9.1.5 Theoretical and Algorithmic Details
300(2)
9.1.6 Summary Comments
302(1)
9.2 Bayesian Methods for Network-Structured Genomics Data
303(13)
Stefano Monni
Hongzhe Li
9.2.1 Bayesian Variable Selection with a Markov Random Field Prior
304(5)
9.2.2 Numerical Examples
309(6)
9.2.3 Discussion and Future Direction
315(1)
9.3 Bayesian Phylogenetics
316(11)
Erik W. Bloomquist
Marc A. Suchard
9.3.1 Statistical Phyloalignment
319(2)
9.3.2 Multilocus Data
321(3)
9.3.3 Looking Ahead
324(3)
10 Bayesian Data Mining and Machine Learning
327(50)
10.1 Bayesian Model-based Principal Component Analysis
327(19)
Bani K. Mallick
Shubhankar Ray
Soma Dhavala
10.1.1 Random Principal Components
329(2)
10.1.2 Piecewise RPC Models
331(3)
10.1.3 Principal Components Clustering
334(3)
10.1.4 Reversible Jump Proposals
337(3)
10.1.5 Experimental Results
340(6)
10.2 Priors on the Variance in Sparse Bayesian Learning: the demi-Bayesian Lasso
346(14)
Suhrid Balakrishnan
David Madigan
10.2.1 Background and Notation
347(3)
10.2.2 The demi-Bayesian Lasso
350(4)
10.2.3 Experiments and Results
354(5)
10.2.4 Discussion
359(1)
10.3 Hierarchical Bayesian Mixed-Membership Models and Latent Pattern Discovery
360(17)
Edoardo M. Airoldi
Stephen E. Fienberg
Cyrille J. Joutard
Tanzy M. Love
10.3.1 Characterizing HBMM Models
363(1)
10.3.2 Strategies for Model Choice
364(1)
10.3.3 Case Study: PNAS 1997-2001
365(4)
10.3.4 Case Study: Disability Profiles
369(5)
10.3.5 Summary
374(3)
11 Bayesian Inference in Political Science, Finance, and Marketing Research
377(42)
11.1 Prior Distributions for Bayesian Data Analysis in Political Science
377(6)
Andrew Gelman
11.1.1 Statistics in Political Science
378(1)
11.1.2 Mixture Models and Different Ways of Encoding Prior Information
379(1)
11.1.3 Incorporating Extra Information Using Poststratification
380(1)
11.1.4 Prior Distributions for Varying-Intercept, Varying-Slope Multilevel Regressions
381(1)
11.1.5 Summary
382(1)
11.2 Bayesian Computation in Finance
383(13)
Satadru Hore
Michael Johannes
Hedibert Lopes
Robert E. McCulloch
Nicholas G. Poison
11.2.1 Empirical Bayesian Asset Pricing
384(1)
11.2.2 Bayesian Inference via SMC
385(3)
11.2.3 Bayesian Inference via MCMC
388(8)
11.2.4 Conclusion
396(1)
11.3 Simulation-based-Estimation in Portfolio Selection
396(14)
Eric Jacquier
Nicholas G. Poison
11.3.1 Basic Asset Allocation
398(7)
11.3.2 Optimum Portfolios by MCMC
405(4)
11.3.3 Discussion
409(1)
11.4 Bayesian Multidimensional Scaling and Its Applications in Marketing Research
410(9)
Duncan K.H. Fong
11.4.1 Bayesian Vector MDS Models
412(2)
11.4.2 A Marketing Application
414(2)
11.4.3 Discussion and Future Research
416(3)
12 Bayesian Categorical Data Analysis
419(48)
12.1 Good Smoothing
419(17)
James H. Albert
12.1.1 Good's 1967 Paper
420(6)
12.1.2 Examples of Good Smoothing
426(4)
12.1.3 Smoothing Hitting Rates in Baseball
430(5)
12.1.4 Closing Comments
435(1)
12.2 Bayesian Analysis of Matched Pair Data
436(15)
Malay Ghosh
Bhramar Mukherjee
12.2.1 Item Response Models
437(2)
12.2.2 Bayesian Analysis of Matched Case-Control Data
439(6)
12.2.3 Some Equivalence Results in Matched Case-Control Studies
445(3)
12.2.4 Other Work
448(1)
12.2.5 Conclusion
449(2)
12.3 Bayesian Choice of Links and Computation for Binary Response Data
451(16)
Ming-Hui Chen
Sungduk Kim
Lynn Kuo
Wangang Xie
12.3.1 The Binary Regression Models
451(3)
12.3.2 Prior and Posterior Distributions
454(1)
12.3.3 Computational Development
454(7)
12.3.4 A Case Study
461(3)
12.3.5 Discussion
464(3)
13 Bayesian Geophysical, Spatial and Temporal Statistics
467(46)
13.1 Modeling Spatial Gradients on Response Surfaces
467(17)
Sudipto Banerjee
Alan E. Gelfand
13.1.1 Directional Derivative Processes
469(2)
13.1.2 Mean Surface Gradients
471(2)
13.1.3 Posterior Inference for Gradients
473(2)
13.1.4 Gradients under Spatial Dirichlet Processes
475(2)
13.1.5 Illustration
477(6)
13.1.6 Concluding Remarks
483(1)
13.2 Non-Gaussian Hierarchical Generalized Linear Geostatistical Model Selection
484(13)
Xia Wang
Dipak K. Dey
Sudipto Banerjee
13.2.1 A Review on the Generalized Linear Geostatistical Model
486(1)
13.2.2 Generalized Extreme Value Link Model
487(2)
13.2.3 Prior and Posterior Distributions for the GLGM Model under Different Links
489(1)
13.2.4 A Simulated Data Example
490(2)
13.2.5 Analysis of Celastrus Orbiculatus Data
492(4)
13.2.6 Discussion
496(1)
13.3 Objective Bayesian Analysis for Gaussian Random Fields
497(16)
Victor De Oliveira
13.3.1 Gaussian Random Field Models
498(1)
13.3.2 Integrated Likelihoods
499(1)
13.3.3 Reference Priors
500(3)
13.3.4 Jeffreys Priors
503(2)
13.3.5 Other Spatial Models
505(2)
13.3.6 Further Properties
507(1)
13.3.7 Multi-Parameter Cases
508(3)
13.3.8 Discussion and Some Open Problems
511(2)
14 Posterior Simulation and Monte Carlo Methods
513(42)
14.1 Importance Sampling Methods for Bayesian Discrimination between Embedded Models
513(14)
Jean-Michel Marin
Christian P. Robert
14.1.1 The Pima Indian Benchmark Model
514(3)
14.1.2 The Basic Monte Carlo Solution
517(1)
14.1.3 Usual Importance Sampling Approximations
518(2)
14.1.4 Bridge Sampling Methodology
520(3)
14.1.5 Harmonic Mean Approximations
523(2)
14.1.6 Exploiting Functional Equalities
525(2)
14.1.7 Conclusion
527(1)
14.2 Bayesian Computation and the Linear Model
527(18)
Matthew J. Heaton
James G. Scott
14.2.1 Bayesian Linear Models
529(2)
14.2.2 Algorithms for Variable Selection and Shrinkage
531(6)
14.2.3 Examples
537(8)
14.2.4 Final Remarks
545(1)
14.3 MCMC for Constrained Parameter and Sample Spaces
545(10)
Merrill W. Liechty
John C. Liechty
Peter Muller
14.3.1 The Shadow Prior
547(2)
14.3.2 Example: Modeling Correlation Matrices
549(1)
14.3.3 Simulation Study
550(1)
14.3.4 Classes of Models Suitable for Shadow Prior Augmentations
551(1)
14.3.5 Conclusion
552(3)
References 555(60)
Author Index 615(12)
Subject Index 627
Ming-Hui Chen is Professor of Statistics at the University of Connecticut; Dipak K. Dey is Head and Professor of Statistics at the University of Connecticut; Peter Müller is Professor of Biostatistics at the University of Texas M. D. Anderson Cancer Center; Dongchu Sun is Professor of Statistics at the University of Missouri- Columbia; and Keying Ye is Professor of Statistics at the University of Texas at San Antonio.
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