(EBook PDF) Geometry and Statistics Handbook of Statistics Volume 46 1st edition by Frank Nielsen, Arni Srinivasa Rao, Rao 9780323913461 full chapters

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ISBN-13 :  9780323913461

Author: Frank Nielsen, Arni S.R. Srinivasa Rao, C.R. Rao 

Geometry and Statistics, Volume 46 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors.

Geometry and Statistics – Handbook of Statistics, Volume 46 1st Table of contents:

Section I: Foundations in classical geometry and analysis
Chapter 1: Geometry, information, and complex bundles
Abstract
1: Introduction
2: Complex planes
3: Geometric analysis and Jordan curves
4: Summary
References
Chapter 2: Geometric methods for sampling, optimization, inference, and adaptive agents
Abstract
1: Introduction
2: Accelerated optimization
3: Hamiltonian-based accelerated sampling
4: Statistical inference with kernel-based discrepancies
5: Adaptive agents through active inference
Acknowledgments
References
Chapter 3: Equivalence relations and inference for sparse Markov models
Abstract
1: Introduction
2: Fitting SMMs and example applications
3: Equivalence relations and the computation of distributions of pattern statistics for SMMs
4: Summary
Acknowledgments
References
Section II: Information geometry
Chapter 4: Symplectic theory of heat and information geometry
Abstract
1: Preamble
2: Life and seminal work of Souriau on lie groups thermodynamics
3: From information geometry to lie groups thermodynamics
4: Symplectic structure of fisher metric and entropy as Casimir function in coadjoint representation
5: Covariant maximum entropy density by Souriau model
6: Conclusion
References
Further reading
Chapter 5: A unifying framework for some directed distances in statistics
Abstract
1: Divergences, statistical motivations, and connections to geometry
2: The framework
3: Aggregated/integrated divergences
4: Dependence expressing divergences
5: Bayesian contexts
6: Variational representations
7: Some further variants
Acknowledgments
References
Chapter 6: The analytic dually flat space of the mixture family of two prescribed distinct Cauchy distributions
Abstract
1: Introduction and motivation
2: Differential-geometric structures induced by smooth convex functions
3: Some illustrating examples
4: Information geometry of the mixture family of two distinct Cauchy distributions
5: Conclusion
Appendix: Symbolic computing notebook in MAXIMA
Acknowledgments
References
Chapter 7: Local measurements of nonlinear embeddings with information geometry
Abstract
1: Introduction
2: α-Divergence and autonormalizing
3: α-Discrepancy of an embedding
4: Empirical α-discrepancy
5: Connections to existing methods
6: Conclusion and extensions
Appendices
Appendix A: Proof of Lemma 1
Appendix B: Proof of Proposition 1
Appendix C: Proof of Proposition 2
Appendix D: Proof of Theorem 1
Acknowledgment
References
Section III: Advanced geometrical intuition
Chapter 8: Parallel transport, a central tool in geometric statistics for computational anatomy: Application to cardiac motion modeling
Abstract
1: Introduction
2: Parallel transport with ladder methods
3: Application to cardiac motion modeling
4: Conclusion
Acknowledgments
References
Chapter 9: Geometry and mixture models
Abstract
1: Introduction
2: Identification, singularities, and boundaries
3: Likelihood geometry
4: General geometric structures
5: Singular learning theory
6: Nonstandard testing problems
7: Discussion
References
Chapter 10: Gaussian distributions on Riemannian symmetric spaces of nonpositive curvature
Abstract
1: Introduction
2: Gaussian distributions and RMT
3: Gaussian distributions and Bayesian inference
Appendix A: Riemannian symmetric spaces
Appendix B: Convex optimization
Appendix C: Proofs for Section B
References
Chapter 11: Multilevel contours on bundles of complex planes☆
Abstract
1: Introduction
2: Infinitely many bundles of complex planes
3: Multilevel contours in a random environment
4: Islands and holes in Bℝ(ℂ)
5: Concluding remarks

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