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- W2518620357 abstract "We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class $C_b^k$ with respect to appropriate reference measures. The case $k=infty$, in which the manifolds are modelled on Frechet spaces, is included. The manifolds admit the Fisher-Rao metric and, unusually for the non-parametric setting, Amari's $alpha$-covariant derivatives for all $alphain R$. By construction, they are $C^infty$-embedded submanifolds of particular manifolds of finite measures. The statistical manifolds are dually ($alpha=pm 1$) flat, and admit mixture and exponential representations as charts. Their curvatures with respect to the $alpha$-covariant derivatives are derived. The likelihood function associated with a finite sample is a continuous function on each of the manifolds, and the $alpha$-divergences are of class $C^infty$." @default.
- W2518620357 created "2016-09-16" @default.
- W2518620357 creator A5003073334 @default.
- W2518620357 date "2016-08-13" @default.
- W2518620357 modified "2023-09-27" @default.
- W2518620357 title "Manifolds of Differentiable Densities" @default.
- W2518620357 hasPublicationYear "2016" @default.
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