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2016

Gaussian Approximations for Probability Measures on $\mathbf{R}^d$

Lu, Yulong, Stuart, Andrew M., Weber, Hendrik

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This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence.

Given an admissible target measure, we show the existence of the best approximation, with respect to this divergence, from certain sets of Gaussian measures and Gaussian mixtures.
The asymptotic behavior of such best approximations is then studied in the small parameter limit where the measure concentrates; this asymptotic behaviour is characterized using $\Gamma$-convergence.
The theory developed is then applied to understanding the frequentist consistency of Bayesian inverse problems.

Gaussian Approximations for Probability Measures on $\mathbf{R}^d$ · Around

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1965
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to appear, preprint availble as arXiv:1604.06594

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