Advancements in Bayesian Methods and Implementation, Volume 47 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Fisher Information, Cramer-Rao and Bayesian Paradigm, Compound beta binomial distribution functions, MCMC for GLMMS, Signal Processing and Bayesian, Mathematical theory of Bayesian statistics where all models are wrong, Machine Learning and Bayesian, Non-parametric Bayes, Bayesian testing, and Data Analysis with humans, Variational inference or Functional horseshoe, Generalized Bayes.
1. 1 Introduction - p. 1 2. 2 Gibbs posterior distributions - p. 4 3. 3 Asymptotic theory - p. 14 4. 4 Learning rate selection - p. 20 5. 5 Numerical examples - p. 24 6. 6 Further details - p. 30 7. 7 Conclusion - p. 32 8. Acknowledgments - p. 34 9. References - p. 38 10. Chapter 2: Bayesian selective inference - p. 43 11. Chapter 3: Dependent Bayesian multiple hypothesis testing - p. 67 12. Chapter 4: A new look at Bayesian uncertainty - p. 83 13. Chapter 5: 50 shades of Bayesian testing of hypotheses - p. 103 14. Chapter 6: Inference approach to ground states of quantum systems - p. 121 15. Chapter 7: MCMC for GLMMs - p. 135 16. Abstract - p. 135 17. 1 Introduction - p. 135 18. 2 Likelihood function for GLMMs - p. 136 19. 3 Conditional simulation for GLMMs - p. 138 20. 4 MCMC for Bayesian GLMMs - p. 145 21. 5 A numerical example - p. 151 22. 6 Discussion - p. 156 23. References - p. 157 24. Chapter 8: Sparsity-aware Bayesian inference and its applications - p. 161 25. Abstract - p. 161 26. 1 Introduction - p. 162 27. 2 The hierarchical Bayesian framework - p. 165 28. 3 Joint-sparse signal recovery - p. 173 29. 4 Exploiting intervector correlation - p. 177 30. 5 Intravector correlations: The nested SBL algorithm - p. 186 31. 6 Quantized sparse signal recovery - p. 192 32. 7 Other extensions - p. 198 33. 8 Discussion and future outlook - p. 202 34. References - p. 203 35. Chapter 9: Mathematical theory of Bayesian statistics where all models are wrong - p. 209 36. Abstract - p. 209 37. Abbreviations - p. 209 38. 1 Introduction - p. 209 39. 2 Mathematical theory of Bayesian statistics - p. 211 40. 3 Applications to statistics and machine learning - p. 227 41. 4 Conclusion - p. 235 42. References - p. 236 43. Chapter 10: Geometry in sampling methods: A review on manifold MCMC and particle-based variational inference methods - p. 239 44. Abstract - p. 239 45. 1 Geometry consideration in sampling: Why bother? - p. 239 46. 2 Manifold and related concepts - p. 242 47. 3 Markov chain Monte Carlo on Riemannian manifolds - p. 251 48. 4 Particle-based variational inference methods - p. 260 49. 5 Conclusion - p. 286 50. References - p. 286 51. Index - p. 293
Advancements in Bayesian Methods and Implementation, Volume 47 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Fisher Information, Cramer-Rao and Bayesian Paradigm, Compound beta binomial distribution functions, MCMC for GLMMS, Signal Processing and Bayesian, Mathematical theory of Bayesian statistics where all models are wrong, Machine Learning and Bayesian, Non-parametric Bayes, Bayesian testing, and Data Analysis with humans, Variational inference or Functional horseshoe, Generalized Bayes.
1. 1 Introduction - p. 1 2. 2 Gibbs posterior distributions - p. 4 3. 3 Asymptotic theory - p. 14 4. 4 Learning rate selection - p. 20 5. 5 Numerical examples - p. 24 6. 6 Further details - p. 30 7. 7 Conclusion - p. 32 8. Acknowledgments - p. 34 9. References - p. 38 10. Chapter 2: Bayesian selective inference - p. 43 11. Chapter 3: Dependent Bayesian multiple hypothesis testing - p. 67 12. Chapter 4: A new look at Bayesian uncertainty - p. 83 13. Chapter 5: 50 shades of Bayesian testing of hypotheses - p. 103 14. Chapter 6: Inference approach to ground states of quantum systems - p. 121 15. Chapter 7: MCMC for GLMMs - p. 135 16. Abstract - p. 135 17. 1 Introduction - p. 135 18. 2 Likelihood function for GLMMs - p. 136 19. 3 Conditional simulation for GLMMs - p. 138 20. 4 MCMC for Bayesian GLMMs - p. 145 21. 5 A numerical example - p. 151 22. 6 Discussion - p. 156 23. References - p. 157 24. Chapter 8: Sparsity-aware Bayesian inference and its applications - p. 161 25. Abstract - p. 161 26. 1 Introduction - p. 162 27. 2 The hierarchical Bayesian framework - p. 165 28. 3 Joint-sparse signal recovery - p. 173 29. 4 Exploiting intervector correlation - p. 177 30. 5 Intravector correlations: The nested SBL algorithm - p. 186 31. 6 Quantized sparse signal recovery - p. 192 32. 7 Other extensions - p. 198 33. 8 Discussion and future outlook - p. 202 34. References - p. 203 35. Chapter 9: Mathematical theory of Bayesian statistics where all models are wrong - p. 209 36. Abstract - p. 209 37. Abbreviations - p. 209 38. 1 Introduction - p. 209 39. 2 Mathematical theory of Bayesian statistics - p. 211 40. 3 Applications to statistics and machine learning - p. 227 41. 4 Conclusion - p. 235 42. References - p. 236 43. Chapter 10: Geometry in sampling methods: A review on manifold MCMC and particle-based variational inference methods - p. 239 44. Abstract - p. 239 45. 1 Geometry consideration in sampling: Why bother? - p. 239 46. 2 Manifold and related concepts - p. 242 47. 3 Markov chain Monte Carlo on Riemannian manifolds - p. 251 48. 4 Particle-based variational inference methods - p. 260 49. 5 Conclusion - p. 286 50. References - p. 286 51. Index - p. 293
