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June 2020 A concurrence theorem for alpha-connections on the space of t-distributions and its application
Atsuhide MORI
Hokkaido Math. J. 49(2): 201-214 (June 2020). DOI: 10.14492/hokmj/1602036023

Abstract

The space of Student's t-distributions with $\nu$ degrees of freedom is the upper half-plane $\mathbb H$ with the location-scale coordinates. A normal distribution is a t-distribution with $\nu=\infty$. The $\alpha$-connections for t-distributions form a line ${\mathbb L}^\nu$ in the space of affine connections on $\mathbb H$. We show that the family $\{{\mathbb L}^\nu\}_{\nu\in(1,\infty]}$ has the concurrent point which presents the e-connection for normal distributions. As an application, generalizing the previous result of the author, we construct a contact Hamiltonian flow which visualizes certain Bayesian learnings.

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Atsuhide MORI. "A concurrence theorem for alpha-connections on the space of t-distributions and its application." Hokkaido Math. J. 49 (2) 201 - 214, June 2020. https://doi.org/10.14492/hokmj/1602036023

Information

Published: June 2020
First available in Project Euclid: 7 October 2020

zbMATH: 07276073
MathSciNet: MR4159168
Digital Object Identifier: 10.14492/hokmj/1602036023

Subjects:
Primary: 57R17, 57R30, 62F15

Rights: Copyright © 2020 Hokkaido University, Department of Mathematics

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Vol.49 • No. 2 • June 2020
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