Advancements in Bayesian methods and implementation:
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| Other Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge, MA
Academic Press
[2022]
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| Series: | Handbook of statistics
volume 47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 304 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9780323952682 |
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| adam_text | Contents Contributors Preface 1. 2. Direct Gibbs posterior inference on risk minimizers: Construction, concentration, and calibration xi xiii 1 Ryan Martin and Nicholas Syring 1. Introduction 2. Gibbs posterior distributions 2.1 Problem setup 2.2 Definition 2.3 FAQs 2.4 Illustrations 3. Asymptotic theory 3.1 Objectives and generalstrategies 3.2 Consistency 3.3 Concentration rates 3.4 Distributional approximations 4. Learning rate selection 5. Numerical examples 5.1 Quantile regression 5.2 Classification 5.3 Nonlinear regression 6. Further details 6.1 Things we did not discuss 6.2 Open problems 7. Conclusion Acknowledgments Appendix A.1 Proofs References 1 4 4 6 8 11 14 14 15 16 18 21 24 24 26 28 30 30 31 32 33 34 34 38 Bayesian selective inference 43 Daniel Garcia Rasines and G. Alastair Young 1. Introduction 2. Bayes and selection 2.1 Fixed and random parameters 43 45 48 v
Contents vi 3. 4. 5. 3. Noninformative priors for selective inference 3.1 Noninformative priors for exponential families 4. Discussion References 50 56 64 65 Dependent Bayesian multiple hypothesis testing 67 Noirrit Kiran Chandra and Sourabh Bhattacharya 1. Introduction 2. Bayesian multiple hypothesis testing 2.1 Preliminaries and setup 2.2 The decision problem 3. Dependent multiple testing 3.1 New error based criterion 3.2 Choice of Ci,...,Gm 4. Simulation study 4.1 The postulated Bayesian model 4.2 Comparison criteria 4.3 Comparison of the results 5. Discussion References 67 69 69 71 72 74 75 76 76 77 77 78 79 A new look at Bayesian uncertainty 83 Stephen C. Walker 1. Introduction 2. Missing data 3. Parametric martingale sequences 3.1 Langevin posterior 4. Nonparametric martingale distributions 5. Illustrations 5.1 Parametric case 5.2 Nonparametric case 6. Mathematical theory 7. Discussion Acknowledgments References 83 86 88 90 92 93 93 94 96 98 Ю0 Ίθθ 50 shades of Bayesian testing of hypotheses Christian P. Robert 1. Introduction 2. Bayesian hypothesis testing 3. Improper priors united against hypothesis testing 4. The Jeffreys-Lindley paradox 5. Posterior predictive p-values 6. A modest proposal 7. Conclusion Acknowledgments References 103 103 104 107 109 110 111 116 116 117
Contents 6. Inference approach to ground states of quantum systems vii 121 Angelo Plastino and A.R. Plastino 1. Introduction 121 2. The Jaynes maximum entropy methodology: Brief resume 122 3. The quantum maximum entropy approach 123 3.1 Preliminaries 123 4. Properties of Sq that make our approximate maximum entropy approach wave functions reasonableones 124 4.1 Sq is a true Shannon s ignorance function 124 4.2 Subject to the known quantities bk, themaximum value of Sq is unique 125 4.3 The entropy Sq obeys an H-theorem 125 4.4 Our $Q-ground-state wave functions respect the viriai theorem 126 4.5 The SQ-ground-state wave functions respect hypervirial theorems 127 4.6 Saturation 127 4.7 Speculation 127 5. Coulomb potential 127 5.1 Harmonic oscillator 128 5.2 Morse potential 128 5.3 Ground state of the quartic oscillator 129 5.4 A possible MEM extension 129 6. Noncommuting observables 129 7. Other entropie or information measures 130 8. Conclusions 133 References 133 7. MCMC for GLMMs Vivekananda Roy 1. Introduction 2. Likelihood function for GLMMs 3. Conditional simulation for GLMMs 3.1 MALA for GLMMs 3.2 HMC for GLMMs 3.3 Data augmentation for GLMMs 4. MCMC for Bayesian GLMMs 4.1 MALA and HMC forBayesian GLMMs 4.2 Data augmentationforBayesian GLMMs 5. A numerical example 6. Discussion References 135 135 136 139 139 141 143 147 148 150 154 156 157
viii 8. Contents Sparsity-aware Bayesian inference and its applications Geethu Joseph, Saurabh Khanna, Chandra R. Murthy, Ranjitha Prasad, and Sai Subramanyam Thoota 1. Introduction 1.1 Quick summary of existing methods for sparse signal recovery 163 1.2 Bayesian approaches: Motivation and related literature 164 2. The hierarchical Bayesian framework 2.1 Gaussian scale mixtures and sparse Bayesian learning 166 2.2 SBL framework 2.3 Case study: Wireless channel estimation and SBL 3. Joint-sparse signal recovery 3.1 The MSBL algorithm 3.2 Expectation maximization in MSBL 3.3 An interesting interpretation of the MSBL cost function 174 3.4 A Covariance-matching framework for sparse support recovery using MMVs 175 3.5 Examples of covariance-matching algorithms for sparse support recovery 117 4. Exploiting intervector correlation 4.1 Intervector correlation: TheKalman SBLalgorithm 4.2 Online sparse vector recovery 4.3 Case study (continued):Wirelesschannel estimation and the KSBL algorithm 5. Intravector correlations: The nested SBL algorithm 5.1 Nested SBL (ß ƒ/s) 6. Quantized sparse signal recovery 7. Other extensions 7.1 Decentralized SBL 7.2 Dictionary learning 7.3 Relationship with robust principal component analysis and sparse + low-rank decomposition 200 7.4 Deep unfolded SBL 8. Discussion and future outlook References 9. 161 162 165 167 169 173 173 174 178 179 181 185 186 189 192 198 198 199 202 202 203 Mathematical theory of Bayesian statistics where all models are wrong 209 Sumio Watanabe 1. Introduction 2. Mathematical theory of Bayesian statistics 2.1 DGP, model, and
prior 2.2 Generalization loss and free energy 209 211 211 213
Contents 2.3 Regular theory 2.4 Singular theory 2.5 Phase transitions 3. Applications to statistics and machine learning 3.1 Model evaluation 3.2 Prior evaluation 3.3 Not i.i.d. cases 4. Conclusion References ix 217 220 225 227 227 230 232 235 236 10. Geometry in sampling methods: A review on manifold MCMC and particle-based variational inference methods 239 Chang Liu and Jun Zhu 1. Geometry consideration in sampling: Why bother? 2. Manifold and related concepts 2.1 Manifold 2.2 Tangent vector and vector field 2.3 Cotangent vector and differential form 2.4 Riemannian manifold 2.5 Measure 2.6 Divergence and Laplacian 2.7 Manifold embedding 3. Markov chain Monte Carlo on Riemannian manifolds 3.1 Technical description of general MCMCdynamics 3.2 Riemannian MCMC in coordinate space 3.3 Riemannian MCMC in embedded space 4. Particle-based variational inference methods 4.1 Stein variational gradient descent 4.2 The Wasserstein space 4.3 Geometric view of particle-based variationalinference methods 4.4 Geometric view of MCMC dynamics and relation to ParVI methods 4.5 Variants and Techniques Inspired by theGeometric View 5. Conclusion Acknowledgments References Index 239 242 242 244 246 247 248 249 250 251 252 253 258 260 261 262 266 270 277 286 286 286 295
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| adam_txt |
Contents Contributors Preface 1. 2. Direct Gibbs posterior inference on risk minimizers: Construction, concentration, and calibration xi xiii 1 Ryan Martin and Nicholas Syring 1. Introduction 2. Gibbs posterior distributions 2.1 Problem setup 2.2 Definition 2.3 FAQs 2.4 Illustrations 3. Asymptotic theory 3.1 Objectives and generalstrategies 3.2 Consistency 3.3 Concentration rates 3.4 Distributional approximations 4. Learning rate selection 5. Numerical examples 5.1 Quantile regression 5.2 Classification 5.3 Nonlinear regression 6. Further details 6.1 Things we did not discuss 6.2 Open problems 7. Conclusion Acknowledgments Appendix A.1 Proofs References 1 4 4 6 8 11 14 14 15 16 18 21 24 24 26 28 30 30 31 32 33 34 34 38 Bayesian selective inference 43 Daniel Garcia Rasines and G. Alastair Young 1. Introduction 2. Bayes and selection 2.1 Fixed and random parameters 43 45 48 v
Contents vi 3. 4. 5. 3. Noninformative priors for selective inference 3.1 Noninformative priors for exponential families 4. Discussion References 50 56 64 65 Dependent Bayesian multiple hypothesis testing 67 Noirrit Kiran Chandra and Sourabh Bhattacharya 1. Introduction 2. Bayesian multiple hypothesis testing 2.1 Preliminaries and setup 2.2 The decision problem 3. Dependent multiple testing 3.1 New error based criterion 3.2 Choice of Ci,.,Gm 4. Simulation study 4.1 The postulated Bayesian model 4.2 Comparison criteria 4.3 Comparison of the results 5. Discussion References 67 69 69 71 72 74 75 76 76 77 77 78 79 A new look at Bayesian uncertainty 83 Stephen C. Walker 1. Introduction 2. Missing data 3. Parametric martingale sequences 3.1 Langevin posterior 4. Nonparametric martingale distributions 5. Illustrations 5.1 Parametric case 5.2 Nonparametric case 6. Mathematical theory 7. Discussion Acknowledgments References 83 86 88 90 92 93 93 94 96 98 Ю0 Ίθθ 50 shades of Bayesian testing of hypotheses Christian P. Robert 1. Introduction 2. Bayesian hypothesis testing 3. Improper priors united against hypothesis testing 4. The Jeffreys-Lindley paradox 5. Posterior predictive p-values 6. A modest proposal 7. Conclusion Acknowledgments References 103 103 104 107 109 110 111 116 116 117
Contents 6. Inference approach to ground states of quantum systems vii 121 Angelo Plastino and A.R. Plastino 1. Introduction 121 2. The Jaynes' maximum entropy methodology: Brief resume 122 3. The quantum maximum entropy approach 123 3.1 Preliminaries 123 4. Properties of Sq that make our approximate maximum entropy approach wave functions reasonableones 124 4.1 Sq is a true Shannon's ignorance function 124 4.2 Subject to the known quantities bk, themaximum value of Sq is unique 125 4.3 The entropy Sq obeys an H-theorem 125 4.4 Our $Q-ground-state wave functions respect the viriai theorem 126 4.5 The SQ-ground-state wave functions respect hypervirial theorems 127 4.6 Saturation 127 4.7 Speculation 127 5. Coulomb potential 127 5.1 Harmonic oscillator 128 5.2 Morse potential 128 5.3 Ground state of the quartic oscillator 129 5.4 A possible MEM extension 129 6. Noncommuting observables 129 7. Other entropie or information measures 130 8. Conclusions 133 References 133 7. MCMC for GLMMs Vivekananda Roy 1. Introduction 2. Likelihood function for GLMMs 3. Conditional simulation for GLMMs 3.1 MALA for GLMMs 3.2 HMC for GLMMs 3.3 Data augmentation for GLMMs 4. MCMC for Bayesian GLMMs 4.1 MALA and HMC forBayesian GLMMs 4.2 Data augmentationforBayesian GLMMs 5. A numerical example 6. Discussion References 135 135 136 139 139 141 143 147 148 150 154 156 157
viii 8. Contents Sparsity-aware Bayesian inference and its applications Geethu Joseph, Saurabh Khanna, Chandra R. Murthy, Ranjitha Prasad, and Sai Subramanyam Thoota 1. Introduction 1.1 Quick summary of existing methods for sparse signal recovery 163 1.2 Bayesian approaches: Motivation and related literature 164 2. The hierarchical Bayesian framework 2.1 Gaussian scale mixtures and sparse Bayesian learning 166 2.2 SBL framework 2.3 Case study: Wireless channel estimation and SBL 3. Joint-sparse signal recovery 3.1 The MSBL algorithm 3.2 Expectation maximization in MSBL 3.3 An interesting interpretation of the MSBL cost function 174 3.4 A Covariance-matching framework for sparse support recovery using MMVs 175 3.5 Examples of covariance-matching algorithms for sparse support recovery 117 4. Exploiting intervector correlation 4.1 Intervector correlation: TheKalman SBLalgorithm 4.2 Online sparse vector recovery 4.3 Case study (continued):Wirelesschannel estimation and the KSBL algorithm 5. Intravector correlations: The nested SBL algorithm 5.1 Nested SBL (ß ƒ/s) 6. Quantized sparse signal recovery 7. Other extensions 7.1 Decentralized SBL 7.2 Dictionary learning 7.3 Relationship with robust principal component analysis and sparse + low-rank decomposition 200 7.4 Deep unfolded SBL 8. Discussion and future outlook References 9. 161 162 165 167 169 173 173 174 178 179 181 185 186 189 192 198 198 199 202 202 203 Mathematical theory of Bayesian statistics where all models are wrong 209 Sumio Watanabe 1. Introduction 2. Mathematical theory of Bayesian statistics 2.1 DGP, model, and
prior 2.2 Generalization loss and free energy 209 211 211 213
Contents 2.3 Regular theory 2.4 Singular theory 2.5 Phase transitions 3. Applications to statistics and machine learning 3.1 Model evaluation 3.2 Prior evaluation 3.3 Not i.i.d. cases 4. Conclusion References ix 217 220 225 227 227 230 232 235 236 10. Geometry in sampling methods: A review on manifold MCMC and particle-based variational inference methods 239 Chang Liu and Jun Zhu 1. Geometry consideration in sampling: Why bother? 2. Manifold and related concepts 2.1 Manifold 2.2 Tangent vector and vector field 2.3 Cotangent vector and differential form 2.4 Riemannian manifold 2.5 Measure 2.6 Divergence and Laplacian 2.7 Manifold embedding 3. Markov chain Monte Carlo on Riemannian manifolds 3.1 Technical description of general MCMCdynamics 3.2 Riemannian MCMC in coordinate space 3.3 Riemannian MCMC in embedded space 4. Particle-based variational inference methods 4.1 Stein variational gradient descent 4.2 The Wasserstein space 4.3 Geometric view of particle-based variationalinference methods 4.4 Geometric view of MCMC dynamics and relation to ParVI methods 4.5 Variants and Techniques Inspired by theGeometric View 5. Conclusion Acknowledgments References Index 239 242 242 244 246 247 248 249 250 251 252 253 258 260 261 262 266 270 277 286 286 286 295 |
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| spelling | Advancements in Bayesian methods and implementation edited by Arni S.R. Srinivasa Rao, G. Alastair Young, C.R. Rao Cambridge, MA Academic Press [2022] © 2022 xv, 304 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Handbook of statistics volume 47 Implementation (DE-588)4026661-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Statistik (DE-588)4056995-0 s Bayes-Verfahren (DE-588)4204326-8 s Implementation (DE-588)4026661-8 s DE-604 Rao, Arni S. R. Srinivasa (DE-588)1143256220 edt Young, G. Alastair (DE-588)173811787 edt Rao, C.R. edt Handbook of statistics volume 47 (DE-604)BV000002510 47 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033913403&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Advancements in Bayesian methods and implementation |
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| title_full | Advancements in Bayesian methods and implementation edited by Arni S.R. Srinivasa Rao, G. Alastair Young, C.R. Rao |
| title_fullStr | Advancements in Bayesian methods and implementation edited by Arni S.R. Srinivasa Rao, G. Alastair Young, C.R. Rao |
| title_full_unstemmed | Advancements in Bayesian methods and implementation edited by Arni S.R. Srinivasa Rao, G. Alastair Young, C.R. Rao |
| title_short | Advancements in Bayesian methods and implementation |
| title_sort | advancements in bayesian methods and implementation |
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