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An infinite-dimensional statistical manifold modelled on Hilbert space

<13> This article is the first to construct infinite-dimensional Hilbert manifolds of probability measures generalizing the Fisher-Rao information geometry of finite dimensions. Information manifolds are the natural state spaces for problems in Data Fusion/Assimilation, since their metrics quantify approximation errors in the correct way. Hilbert manifolds are considerably easier to apply than the exponential Orlicz manifold that dominated the research literature for more than a decade. They are the ideal setting for the stochastic differential equations of nonlinear filtering.