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Handbook of Bayesian Variable Selection [Kõva köide]

Edited by (Rice University, Houston, Texas, USA), Edited by (Georgetown University, Washington, Distric of Columbia, USA)
  • Formaat: Hardback, 490 pages, kõrgus x laius: 254x178 mm, kaal: 1420 g, 21 Tables, black and white; 91 Line drawings, black and white; 91 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Handbooks of Modern Statistical Methods
  • Ilmumisaeg: 21-Dec-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367543761
  • ISBN-13: 9780367543761
Teised raamatud teemal:
Handbook of Bayesian Variable SelectionSuurem pilt
  • Formaat: Hardback, 490 pages, kõrgus x laius: 254x178 mm, kaal: 1420 g, 21 Tables, black and white; 91 Line drawings, black and white; 91 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Handbooks of Modern Statistical Methods
  • Ilmumisaeg: 21-Dec-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367543761
  • ISBN-13: 9780367543761
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367543761.html
Märksõnad:
Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed.

The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions.

Features:





Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material
Preface xv
Biography xvii
List of Contributors
xix
List of Symbols
xxi
I Spike-and-Slab Priors
1(130)
1 Discrete Spike-and-Slab Priors: Models and Computational Aspects
3(22)
Marina Vannucci
1.1 Introduction
4(1)
1.2 Spike-and-Slab Priors for Linear Regression Models
4(4)
1.2.1 Stochastic Search MCMC
7(1)
1.2.2 Prediction via Bayesian Model Averaging
8(1)
1.3 Spike-and-Slab Priors for Non-Gaussian Data
8(3)
1.3.1 Compositional Count Data
9(2)
1.4 Structured Spike-and-Slab Priors for Biomedical Studies
11(4)
1.4.1 Network Priors
13(1)
1.4.2 Spiked Nonparametric Priors
14(1)
1.5 Scalable Bayesian Variable Selection
15(3)
1.5.1 Variational Inference
17(1)
1.6 Conclusion
18(1)
Bibliography
19(6)
2 Recent Theoretical Advances with the Discrete Spike-and-Slab Priors
25(32)
Shuang Zhou
Debdeep Pati
2.1 Introduction
26(1)
2.2 Optimal Recovery in Gaussian Sequence Models
27(5)
2.2.1 Minimax Rate in Nearly Black Gaussian Mean Models
27(1)
2.2.2 Optimal Bayesian Recovery in lq-norm
28(3)
2.2.3 Optimal Contraction Rate for Other Variants of Priors
31(1)
2.2.4 Slow Contraction Rate for Light-tailed Priors
32(1)
2.3 Sparse Linear Regression Model
32(9)
2.3.1 Prior Construction and Assumptions
33(1)
2.3.2 Compatibility Conditions on the Design Matrix
34(2)
2.3.3 Posterior Contraction Rate
36(1)
2.3.4 Variable Selection Consistency
37(1)
2.3.5 Variable Selection with Discrete Spike and Zellner's g-Priors
38(1)
2.3.6 Bernstein-von Mises Theorem for the Posterior Distribution
39(2)
2.4 Extension to Generalized Linear Models
41(9)
2.4.1 Construction of the GLM Family
42(1)
2.4.2 Clipped GLM and Connections to Regression Settings
42(2)
2.4.3 Construction of Sparsity Favoring Prior
44(1)
2.4.4 Assumptions on Data Generating Distribution and Prior
45(3)
2.4.5 Adaptive Rate-Optimal Posterior Contraction Rate in ^-norm
48(2)
2.5 Optimality Results for Variational Inference in Linear Regression Models
50(2)
2.6 Discussion
52(1)
Bibliography
53(4)
3 Theoretical and Computational Aspects of Continuous Spike-and-Slab Priors
57(24)
Naveen N. Narisetty
3.1 Introduction
58(1)
3.2 Variable Selection in Linear Models
58(2)
3.3 Continuous Spike-and-Slab Priors
60(1)
3.3.1 Shrinking and Diffusing Priors
60(1)
3.3.2 Spike-and-Slab LASSO
61(1)
3.4 Theoretical Properties
61(7)
3.4.1 Variable Selection Consistency
62(1)
3.4.2 Novel Insights
63(3)
3.4.3 Examples
66(2)
3.5 Computations
68(4)
3.5.1 Skinny Gibbs for Scalable Posterior Sampling
68(2)
3.5.2 Skinny Gibbs for Non-Normal Spike-and-Slab Priors
70(2)
3.6 Generalizations
72(1)
3.7 Conclusion
72(5)
Bibliography
77(4)
4 Spike-and-Slab Meets LASSO: A Review of the Spike-and-Slab LASSO
81(28)
Ray Bai
Veronika Rockova
Edward I. George
4.1 Introduction
82(1)
4.2 Variable Selection in High-Dimensions: Frequentist and Bayesian Strategies
83(2)
4.2.1 Penalized Likelihood Approaches
83(1)
4.2.2 Spike-and-Slab Priors
84(1)
4.3 The Spike-and-Slab LASSO
85(4)
4.3.1 Prior Specification
85(1)
4.3.2 Selective Shrinkage and Self-Adaptivity to Sparsity
86(2)
4.3.3 The Spike-and-Slab LASSO in Action
88(1)
4.4 Computational Details
89(3)
4.4.1 Coordinate-wise Optimization
89(2)
4.4.2 Dynamic Posterior Exploration
91(1)
4.4.3 EM Implementation of the Spike-and-Slab LASSO
91(1)
4.5 Uncertainty Quantification
92(1)
4.5.1 Debiasing the Posterior Mode
92(1)
4.5.2 Posterior Sampling for the Spike-and-Slab LASSO
93(1)
4.6 Illustrations
93(3)
4.6.1 Example on Synthetic Data
93(2)
4.6.2 Bardet-Beidl Syndrome Gene Expression Study
95(1)
4.7 Methodological Extensions
96(4)
4.8 Theoretical Properties
100(1)
4.9 Discussion
101(2)
Bibliography
103(6)
5 Adaptive Computational Methods for Bayesian Variable Selection
109(22)
Jim E. Griffin
Mark F. J. Steel
5.1 Introduction
109(3)
5.1.1 Some Reasons to be Cheerful Ill
5.1.2 Adaptive Monte Carlo Methods
112(1)
5.2 Some Adaptive Approaches to Bayesian Variable Selection
112(1)
5.3 Two Adaptive Algorithms
113(4)
5.3.1 Linear Regression
115(1)
5.3.2 Non-Gaussian Models
116(1)
5.4 Examples
117(8)
5.4.1 Simulated Example: Linear Regression
117(2)
5.4.2 Fine Mapping for Systemic Lupus Erythematosus
119(2)
5.4.3 Analysing Environmental DNA Data
121(4)
5.5 Discussion
125(2)
Bibliography
127(4)
II Continuous Shrinkage Priors
131(68)
6 Theoretical Guarantees for the Horseshoe and Other Global-Local Shrinkage Priors
133(28)
Stephanie van der Pas
6.1 Introduction
134(3)
6.1.1 Model and Notation
134(1)
6.1.2 Global-Local Shrinkage Priors and Spike-and-Slab Priors
134(1)
6.1.3 Performance Measures
135(2)
6.2 Global-Local Shrinkage Priors
137(2)
6.3 Recovery Guarantees
139(10)
6.3.1 Non-Adaptive Posterior Concentration Theorems
140(3)
6.3.2 Proof Techniques
143(2)
6.3.3 Adaptive Posterior Concentration Theorems
145(2)
6.3.4 Other Sparsity Assumptions
147(1)
6.3.5 Implications for Practice
147(2)
6.4 Uncertainty Quantification Guarantees
149(3)
6.4.1 Credible Intervals
149(2)
6.4.2 Credible Balls
151(1)
6.4.3 Implications for Practice
152(1)
6.5 Variable Selection Guarantees
152(2)
6.5.1 Thresholding on the Amount of Shrinkage
152(1)
6.5.2 Checking for Zero in Marginal Credible Intervals
153(1)
6.6 Discussion
154(1)
Bibliography
155(6)
7 MCMC for Global-Local Shrinkage Priors in High-Dimensional Settings
161(18)
Anirban Bhattacharya
James Johndrow
7.1 Introduction
161(1)
7.2 Global-Local Shrinkage Priors
162(1)
7.3 Posterior Sampling
163(8)
7.3.1 Sampling Structured High-Dimensional Gaussians
164(3)
7.3.2 Blocking can be Advantageous
167(2)
7.3.3 Geometric Convergence
169(2)
7.4 Approximate MCMC
171(2)
7.5 Conclusion
173(2)
Bibliography
175(4)
8 Variable Selection with Shrinkage Priors via Sparse Posterior Summaries
179(20)
Yan Dora Zhang
Weichang Yu
Howard D. Bondell
8.1 Introduction
180(1)
8.2 Penalized Credible Region Selection
180(6)
8.2.1 Gaussian Prior
181(1)
8.2.2 Global-Local Shrinkage Priors
182(2)
8.2.3 Example: Simulation Studies
184(1)
8.2.4 Example: Mouse Gene Expression Real-time PCR
185(1)
8.3 Approaches Based on Other Posterior Summaries
186(1)
8.4 Model Selection for Logistic Regression
187(1)
8.5 Graphical Model Selection
188(2)
8.6 Confounder Selection
190(2)
8.7 Time-Varying Coefficients
192(1)
8.8 Discussion
193(2)
Bibliography
195(4)
III Extensions to Various Modeling Frameworks
199(150)
9 Bayesian Model Averaging in Causal Inference
201(26)
Joseph Antonelli
Francesca Dominici
9.1 Introduction to Causal Inference
202(4)
9.1.1 Potential Outcomes, Estimands, and Identifying Assumptions
203(1)
9.1.2 Estimation Strategies Using Outcome Regression, Propensity Scores, or Both
204(1)
9.1.3 Why Use BMA for Causal Inference?
205(1)
9.2 Failure of Traditional Model Averaging for Causal Inference Problems
206(2)
9.3 Prior Distributions Tailored Towards Causal Estimation
208(4)
9.3.1 Bayesian Adjustment for Confounding Prior
209(2)
9.3.2 Related Prior Distributions that Link Treatment and Outcome Models
211(1)
9.4 Bayesian Estimation of Treatment Effects
212(5)
9.4.1 Outcome Model Based Estimation
212(1)
9.4.2 Incorporating the Propensity Score into the Outcome Model
213(1)
9.4.3 BMA Coupled with Traditional Frequentist Estimators
214(1)
9.4.4 Analysis of Volatile Compounds on Cholesterol Levels
215(2)
9.5 Assessment of Uncertainty
217(2)
9.6 Extensions to Shrinkage Priors and Nonlinear Regression Models
219(2)
9.7 Conclusion
221(2)
Bibliography
223(4)
10 Variable Selection for Hierarchically-Related Outcomes: Models and Algorithms
227(24)
Helene Ruffieux
Leonardo Bottolo
Sylvia Richardson
10.1 Introduction
228(1)
10.2 Model Formulations, Computational Challenges and Tradeoffs
229(5)
10.3 Illustrations on Published Case Studies
234(7)
10.3.1 Modelling eQTL Signals across Multiple Tissues
234(4)
10.3.2 Modelling eQTL Hotspots under Different Experimental Conditions
238(3)
10.4 Discussion
241(4)
Bibliography
245(6)
11 Bayesian Variable Selection in Spatial Regression Models
251(20)
Brian J. Reich
Ana-Maria Staicu
11.1 Introduction
251(1)
11.2 Spatial Regression
252(1)
11.3 Regression Coefficients as Spatial Processes
253(2)
11.3.1 Spatially-Varying Coefficient Model
253(1)
11.3.2 Scalar-on-Image Regression
254(1)
11.4 Sparse Spatial Processes
255(6)
11.4.1 Discrete Mixture Priors
256(4)
11.4.2 Continuous Shrinkage Priors
260(1)
11.5 Application to Microbial Fungi across US Households
261(1)
11.6 Discussion
262(5)
Bibliography
267(4)
12 Effect Selection and Regularization in Structured Additive Distributional Regression
271(26)
Paul Wiemann
Thomas Kneib
Helga Wagner
12.1 Introduction
272(1)
12.2 Structured Additive Distributional Regression
273(4)
12.2.1 Basic Model Structure
273(2)
12.2.2 Predictor Components
275(1)
12.2.3 Common Response Distributions
276(1)
12.2.4 Basic MCMC Algorithm
276(1)
12.3 Effect Selection Priors
277(5)
12.3.1 Challenges
277(1)
12.3.2 Spike-and-Slab Priors for Effect Selection
278(3)
12.3.3 Regularization Priors for Effect Selection
281(1)
12.4 Application: Childhood Undernutrition in India
282(6)
12.4.1 Data
282(1)
12.4.2 A Main Effects Location-Scale Model
283(3)
12.4.3 Decomposing an Interaction Surface
286(2)
12.5 Other Regularization Priors for Functional Effects
288(3)
12.5.1 Locally Adaptive Regularization
288(1)
12.5.2 Shrinkage towards a Functional Subspace
289(2)
12.6 Summary and Discussion
291(2)
Bibliography
293(4)
13 Sparse Bayesian State-Space and Time-Varying Parameter Models
297(30)
Sylvia Fruhwirth-Schnatter
Peter Knaus
13.1 Introduction
298(1)
13.2 Univariate Time-Varying Parameter Models
299(4)
13.2.1 Motivation and Model Definition
299(2)
13.2.2 The Inverse Gamma Versus the Ridge Prior
301(2)
13.2.3 Gibbs Sampling in the Non-Centered Parametrization
303(1)
13.3 Continuous Shrinkage Priors for Sparse TVP Models
303(7)
13.3.1 From the Ridge Prior to Continuous Shrinkage Priors
303(4)
13.3.2 Efficient MCMC Inference
307(1)
13.3.3 Application to US Inflation Modelling
308(2)
13.4 Spike-and-Slab Priors for Sparse TVP Models
310(5)
13.4.1 From the Ridge prior to Spike-and-Slab Priors
310(3)
13.4.2 Model Space MCMC
313(1)
13.4.3 Application to US Inflation Modelling
314(1)
13.5 Extensions
315(6)
13.5.1 Including Stochastic Volatility
315(1)
13.5.2 Sparse TVP Models for Multivariate Time Series
316(2)
13.5.3 Non-Gaussian Outcomes
318(1)
13.5.4 Log Predictive Scores for Comparing Shrinkage Priors
318(2)
13.5.5 BMA Versus Continuous Shrinkage Priors
320(1)
13.6 Discussion
321(2)
Bibliography
323(4)
14 Bayesian Estimation of Single and Multiple Graphs
327(22)
Christine B. Peterson
Francesco C. Stingo
14.1 Introduction
328(1)
14.2 Bayesian Approaches for Single Graph Estimation
328(3)
14.2.1 Background on Graphical Models
328(1)
14.2.2 Bayesian Priors for Undirected Networks
329(1)
14.2.3 Bayesian Priors for Directed Networks
330(1)
14.2.4 Bayesian Network Inference for Non-Gaussian Data
331(1)
14.3 Multiple Graphs with Shared Structure
331(5)
14.3.1 Likelihood
332(1)
14.3.2 Prior Formulation
332(1)
14.3.3 Simulation and Case Studies
333(3)
14.3.4 Related Work
336(1)
14.4 Multiple Graphs with Shared Edge Values
336(5)
14.4.1 Likelihood
337(1)
14.4.2 Prior Formulation
337(2)
14.4.3 Analysis of Neuroimaging Data
339(2)
14.5 Multiple DAGs and Other Multiple Graph Approaches
341(1)
14.6 Related Topics
342(1)
14.7 Discussion
343(2)
Bibliography
345(4)
IV Other Approaches to Bayesian Variable Selection
349(112)
15 Bayes Factors Based on g-Priors for Variable Selection
351(20)
Gonzalo Garcia-Donato
Mark F. J. Steel
15.1 Bayes Factors
351(3)
15.2 Variable Selection in the Gaussian Linear Model
354(9)
15.2.1 Objective Prior Specifications
354(2)
15.2.2 Numerical Issues
356(1)
15.2.3 BayesVarSel and Applications
357(4)
15.2.4 Sensitivity to Prior Inputs
361(2)
15.3 Variable Selection for Non-Gaussian Data
363(2)
15.3.1 glmBfp and Applications
364(1)
15.4 Conclusion
365(2)
Bibliography
367(4)
16 Balancing Sparsity and Power: Likelihoods, Priors, and Misspeciflcation
371(24)
David Rossell
Francisco Javier Rubio
16.1 Introduction
372(1)
16.2 BMS in Regression Models
373(2)
16.3 Interpreting BMS Under Misspeciflcation
375(1)
16.4 Priors
376(1)
16.5 Prior Elicitation and Robustness
377(1)
16.6 Validity of Model Selection Uncertainty
378(1)
16.7 Finite-Dimensional Results
379(1)
16.8 High-Dimensional Results
380(2)
16.9 Balancing Sparsity and Power
382(3)
16.10 Examples
385(4)
16.10.1 Salary
385(2)
16.10.2 Colon Cancer
387(1)
16.10.3 Survival Analysis of Serum Free Light Chain Data
388(1)
16.11 Discussion
389(2)
Bibliography
391(4)
17 Variable Selection and Interaction Detection with Bayesian Additive Regression Trees
395(20)
Carlos M. Carvalho
Edward I. George
P. Richard Hahn
Robert E. McCulloch
17.1 Introduction
396(1)
17.2 BART Overview
396(3)
17.2.1 Specification of the BART Regularization Prior
397(1)
17.2.2 Posterior Calculation and Information Extraction
398(1)
17.3 Model-Free Variable Selection with BART
399(4)
17.3.1 Variable Selection with the Boston Housing Data
400(3)
17.4 Model-Free Interaction Detection with BART
403(2)
17.4.1 Variable Selection and Interaction Detection with the Friedman Simulation Setup
403(1)
17.4.2 Interaction Detection with the Boston Housing Data
404(1)
17.5 A Utility Based Approach to Variable Selection using BART Inference
405(5)
17.5.1 Step 1: BART Inference
407(1)
17.5.2 Step 2: Subset Search
407(1)
17.5.3 Step 3: Uncertainty Assessment
408(2)
17.6 Conclusion
410(3)
Bibliography
413(2)
18 Variable Selection for Bayesian Decision Tree Ensembles
415(26)
Antonio R. Linero
Junliang Du
18.1 Introduction
416(2)
18.1.1 Running Example
416(1)
18.1.2 Possible Strategies
417(1)
18.2 Bayesian Additive Regression Trees
418(3)
18.2.1 Decision Trees and their Priors
418(2)
18.2.2 The BART Model
420(1)
18.3 Variable Importance Scores
421(3)
18.3.1 Empirical Bayes and Variable Importance Scores
421(3)
18.4 Sparsity Inducing Priors on s
424(6)
18.4.1 The Uniform Prior on s
424(1)
18.4.2 The Dirichlet Prior
424(2)
18.4.3 The Spike-and-Forest Prior
426(2)
18.4.4 Finite Gibbs Priors
428(2)
18.5 An Illustration: The WIPP Dataset
430(3)
18.6 Extensions
433(2)
18.6.1 Interaction Detection
433(2)
18.6.2 Structure in Predictors
435(1)
18.7 Discussion
435(2)
Bibliography
437(4)
19 Stochastic Partitioning for Variable Selection in Multivariate Mixture of Regression Models
441(20)
Stefano Monni
Mahlet G. Tadesse
19.1 Introduction
442(1)
19.2 Mixture of Univariate Regression Models
443(3)
19.2.1 Model Fitting
443(2)
19.2.2 Variable Selection
445(1)
19.3 Stochastic Partitioning for Multivariate Mixtures
446(3)
19.3.1 Model Formulation
446(1)
19.3.2 Prior Specification
446(2)
19.3.3 Model Fitting
448(1)
19.3.4 Posterior Inference
448(1)
19.4 Spavs and Application
449(3)
19.4.1 Choice of Hyperparameters and Other Input Values
449(1)
19.4.2 Post-Processing of MCMC Output and Posterior Inference
450(2)
19.5 Discussion
452(5)
Bibliography
457(4)
Index 461
Mahlet Tadesse is Professor and Chair in the Department of Mathematics and Statistics at Georgetown University, USA. Her research over the past two decades has focused on Bayesian modeling for high-dimensional data with an emphasis on variable selection methods and mixture models. She also works on various interdisciplinary projects in genomics and public health. She is a recipient of the Myrto Lefkopoulou Distinguished Lectureship award, an elected member of the International Statistical Institute and an elected fellow of the American Statistical Association.

Marina Vannucci is Noah Harding Professor of Statistics at Rice University, USA. Her research over the past 25 years has focused on the development of methodologies for Bayesian variable selection in linear settings, mixture models and graphical models, and on related computational algorithms. She also has a solid history of scientific collaborations and is particularly interested in applications of Bayesian inference to genomics and neuroscience. She has received an NSF CAREER award and the Mitchell prize by ISBA for her research, and the Zellner Medal by ISBA for exceptional service over an extended period of time with long-lasting impact. She is an elected Member of ISI and RSS and an elected fellow of ASA, IMS, AAAS and ISBA.