Information Geometry: Near Randomness and Near Independence, Issue 1953The main motivation for this book lies in the breadth of applications in which a statistical model is used to represent small departures from, for example, a Poisson process. Our approach uses information geometry to provide a c- mon context but we need only rather elementary material from di?erential geometry, information theory and mathematical statistics. Introductory s- tions serve together to help those interested from the applications side in making use of our methods and results. We have available Mathematica no- books to perform many of the computations for those who wish to pursue their own calculations or developments. Some 44 years ago, the second author ?rst encountered, at about the same time, di?erential geometry via relativity from Weyl's book [209] during - dergraduate studies and information theory from Tribus [200, 201] via spatial statistical processes while working on research projects at Wiggins Teape - searchandDevelopmentLtd-cf. theForewordin[196]and[170,47,58]. H- ing started work there as a student laboratory assistant in 1959, this research environment engendered a recognition of the importance of international c- laboration, and a lifelong research interest in randomness and near-Poisson statistical geometric processes, persisting at various rates through a career mainly involved with global di?erential geometry. From correspondence in the 1960s with Gabriel Kron [4, 124, 125] on his Diakoptics, and with Kazuo Kondo who in?uenced the post-war Japanese schools of di?erential geometry and supervised Shun-ichi Amari's doctorate [6], it was clear that both had a much wider remit than traditionally pursued elsewhere. |
Contents
Mathematical Statistics and Information Theory | 1 |
Introduction to Riemannian Geometry | 19 |
Information Geometry | 31 |
Information Geometry of Bivariate Families | 55 |
group headed by Andrew Doig of the Manchester Interdisciplinary Biocentre | 76 |
Neighbourhoods of Poisson Randomness Independence | 108 |
Cosmological Voids and Galactic Clustering | 119 |
Amino Acid Clustering | 138 |
Other editions - View all
Information Geometry: Near Randomness and Near Independence Khadiga Arwini,C. T. J. Dodson Limited preview - 2008 |
Information Geometry: Near Randomness and Near Independence Khadiga Arwini,C. T. J. Dodson No preview available - 2008 |
Information Geometry: Near Randomness and Near Independence Khadiga Arwini,C. T. J. Dodson No preview available - 2008 |
Common terms and phrases
3-manifold a-connections a-curvature tensor a-Ricci tensor a-scalar curvature a₁ affine immersion amino acids Arwini bivariate gamma distribution bivariate Gaussian C.T.J. Dodson clustering coefficient of variation correlation coefficient corresponds covariance curve cv(x defined distances entropy equation exponential distribution exponential family fibre networks Figure Fisher information metric Fisher metric Freund galaxies gamma density functions gamma distribution gamma manifold Gaussian density functions geodesic given ij,k independent components information geometry log-Gaussian M₁ marginal functions Mathematical maximum likelihood McKay bivariate gamma mutually dual n-manifold natural coordinate system points Poisson process Poisson random polygon pore porous media potential function probability density functions Proposition random variables Riemannian manifolds scalar curvature sequence smooth standard deviation stochastic structure submanifold tangent vector tions unit mean variance vector field void αι βι σι ψ α1 ψ α2