Weyl Prior and Bayesian Statistics

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 [Formula: see text]-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 [Formula: see text]-parallel prior with the parameter [Formula: see text] equaling [Formula: see text] , where n is the dimension of the underlying statistical manifold and the minus sign is a result of conventions used in the definition of [Formula: see text]-connections. This makes the choice for the parameter [Formula: see text] 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.