Abstract
Conjugate prior plays an important role in the field of Bayesian statistics. In fact, families of conjugate priors for various families of distributions have been well-studied and widely used. In this paper, we construct new conjugate priors. More precisely, we give a family of conjugate priors in the explicit form for the family of Poincaré distributions on the upper half plane. Here, Poincaré distributions are essentially the same with the hyperboloid distributions on the 2-dimensional hyperbolic space in the sense of Jensen.
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Acknowledgements
We thank Professor Kei Kobayashi for useful comments. This work was supported by JST, ACT-X Grant Number JPMJAX190K, Japan.
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Tojo, K., Yoshino, T. (2021). An Exponential Family on the Upper Half Plane and Its Conjugate Prior. In: Barbaresco, F., Nielsen, F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning. SPIGL 2020. Springer Proceedings in Mathematics & Statistics, vol 361. Springer, Cham. https://doi.org/10.1007/978-3-030-77957-3_4
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DOI: https://doi.org/10.1007/978-3-030-77957-3_4
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