| Summary: | 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 <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-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 <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-parallel prior with the parameter <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> equaling <inline-formula> <math display="inline"> <semantics> <mrow> <mo>−</mo> <mi>n</mi> </mrow> </semantics> </math> </inline-formula>, where <i>n</i> is the dimension of the underlying statistical manifold and the minus sign is a result of conventions used in the definition of <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-connections. This makes the choice for the parameter <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> 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.
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