Posterior consistency of logistic Gaussian process priors in density estimation |
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Authors: | Surya T. Tokdar Jayanta K. Ghosh |
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Affiliation: | 1. Department of Statistics, Purdue University, USA;2. Division of Theoretical Statistics and Mathematics, Indian Statistical Institute, India |
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Abstract: | We establish weak and strong posterior consistency of Gaussian process priors studied by Lenk [1988. The logistic normal distribution for Bayesian, nonparametric, predictive densities. J. Amer. Statist. Assoc. 83 (402), 509–516] for density estimation. Weak consistency is related to the support of a Gaussian process in the sup-norm topology which is explicitly identified for many covariance kernels. In fact we show that this support is the space of all continuous functions when the usual covariance kernels are chosen and an appropriate prior is used on the smoothing parameters of the covariance kernel. We then show that a large class of Gaussian process priors achieve weak as well as strong posterior consistency (under some regularity conditions) at true densities that are either continuous or piecewise continuous. |
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Keywords: | Gaussian process Logistic transformation Nonparametric density estimation Posterior consistency Sup-norm support |
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