Abstract
A deformed exponential family has two kinds of dual Hessian structures, the U-geometry and the \(\chi \)-geometry. In this paper, we discuss the relation between the non-invariant (F, G)-geometry and the two Hessian structures on a deformed exponential family. A generalized likelihood function called F-likelihood function is defined and proved that the Maximum F-likelihood estimator is a Maximum a posteriori estimator.
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Harsha, K.V., Moosath, K.S.S. (2015). Hessian Structures and Non-invariant (F, G)-Geometry on a Deformed Exponential Family. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_24
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DOI: https://doi.org/10.1007/978-3-319-25040-3_24
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