Classifying histograms of medical data using information geometry of beta distributions

It can be seen The differential geometric approach to probability theory as a natural choice of metric as it is the only Riemannian and statistics has met increasing interest in the past metric that is invariant with respect to transformation by years, from the theoretical point of view as well as in a sufficient statistic, or a diffeomorphic transformation of applications. In this approach, probability distributions the support in the nonparametric case (Cencov, 2000; are seen as elements of a differentiable manifold, on which Bauer et al., 2016). Arguably the most famous example a metric structure is defined through the choice of a of Fisher information geometry of a statistical model is Riemannian metric. Two very important ones are the that of the univariate Gaussian model, which is hyperbolic. Wasserstein metric, central in optimal transport, and The geometries of other parametric families such as the Fisher information metric (also called Fisher-Rao the multivariate Gaussian model (Atkinson and Mitchell, metric), essential in information geometry. Unlike optimal 1981; Skovgaard, 1984), the family of gamma distributions transport, information geometry is foremost concerned (Arwini and Dodson, 2008; Rebbah et al., 2019), or more with parametric families of probability distributions, and generally location-scale models (Said et al., 2019), among defines a Riemannian structure on the parameter space others, have also received a lot of attention.