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In mathematics, a statistical manifold is a Riemannian manifold, each of whose points is a probability distribution. Statistical manifolds provide a setting for the field of information geometry. The Fisher information metric provides a metric on these manifolds. Following this definition, the log-likelihood function is a differentiable map and the score is an inclusion.[1]
- ^ Murray, Michael K.; Rice, John W. (1993). "The definition of a statistical manifold". Differential Geometry and Statistics. Chapman & Hall. pp. 76–77. ISBN 0-412-39860-5.