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The 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.
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