Title




Information geometry under monotone embedding. Part II: geometry


Author






Abstract




The rhotau embedding of a parametric statistical model defines both a Riemannian metric, called "rhotau metric", and an alpha family of rhotau connections. We give a set of equivalent conditions for such a metric to become Hessian and for the +/ 1connections to be dually flat. Next we argue that for any choice of strictly increasing functions rho(u) and tau(u) one can construct a statistical model which is Hessian and phiexponential. The metric derived from the escort expectations is conformally equivalent with the rhotau metric. 


Language




English


Source (journal)




Lecture notes in computer science.  Berlin, 1973, currens


Source (book)




3rd International SEE Conference on Geometric Science of Information, (GSI), NOV 0709, 2017, Paris, FRANCE


Publication




Cham
:
Springer international publishing ag
,
2017


ISBN




9783319684444






9783319684451
9783319684444


DOI




10.1007/9783319684451_25


Volume/pages




10589
(2017)
, p. 215222


ISI




000440482500025


Full text (Publisher's DOI)





