Abstract
The rho-tau embedding of a parametric statistical model defines both a Riemannian metric, called “rho-tau metric”, and an alpha family of rho-tau connections. We give a set of equivalent conditions for such a metric to become Hessian and for the \(\pm 1\)-connections 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 phi-exponential. The metric derived from the escort expectations is conformally equivalent with the rho-tau metric.
J. Naudts and J. Zhang contributed equally to this paper.
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Acknowledgement
The second author is supported by DARPA/ARO Grant W911NF-16-1-0383.
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Naudts, J., Zhang, J. (2017). Information Geometry Under Monotone Embedding. Part II: Geometry. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_25
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DOI: https://doi.org/10.1007/978-3-319-68445-1_25
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