Bayesian Density Estimation
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We develop a fully Bayesian solution to the density estimation problem. Smoothness of the estimates f is incorporated through the integral formulation f(x) = ∫ dx′ф(x′) K(x,x′) involving an appropriately smooth kernel function K. The analysis involves integration over the underlying space of densities ф. The key to this approach lies in properly setting up a measure on this space consistent with passage to the continuum limit of continuous x. With this done, a flat prior suffices to complete a well-posed definition of the problem.
KeywordsContinuum Limit Dirichlet Form Hypothesis Space Optimal Width Bayesian Solution
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