Bayesian Density Estimation
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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- Neal, R. M. (1992). Bayesian mixture modelling. In Maximum Entropy and Bayesian Methods (eds C. R. Smith, G. J. Erickson and P. O. Neudorfer ), 197 – 211, Dordrecht: Kluwer.Google Scholar
- Powell, M. J. D. (1987). Radial basis functions for multivariable interpolation: a review. In Algorithms for Approximation(eds J. C. Mason and M. G. Cox ), 143 – 167, Oxford: Clarendon.Google Scholar
- West, M. (1992). Modelling with mixtures. In Bayesian Statistics 4(eds J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith ), 503–524, Oxford: Clarendon.Google Scholar