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Weyl Prior and Bayesian Statistics

Multidisciplinary Digital Publishing Institute

When using Bayesian inference, one needs to choose a prior distribution for parameters. The well-known Jeffreys prior is based on the Riemann metric tensor on a statistical manifold. Takeuchi and Amari defined the α-parallel prior, which generalized the Jeffreys prior by exploiting a higher-order geometric object, known as a Chentsov–Amari tensor. In this paper, we propose a new prior based on the Weyl structure on a statistical manifold. It turns out that our prior is a special case of the α-parallel prior with the parameter α equaling −n, where n is the dimension of the underlying statistical manifold and the minus sign is a result of conventions used in the definition of α-connections. This makes the choice for the parameter α more canonical. We calculated the Weyl prior for univariate Gaussian and multivariate Gaussian distribution. The Weyl prior of the univariate Gaussian turns out to be the uniform prior.

Article

eng

Vancouver : University of British Columbia Library

10.14288/1.0390016

Arts and Sciences, Irving K. Barber School of (Okanagan); Non UBC; Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)

10.3390/e22040467

Faculty

DSpace