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Saddlepoint approximation for mixture models
Institute of Mathematics, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland anthony.davison{at}epfl.ch mastropi{at}uwalumni.com
Received for publication 1 April 2008. Revision received 1 October 2008.
Two-component mixture distributions with one component a point mass and the other a continuous density may be used as priors for Bayesian inference when sparse representation of an underlying signal is required. We show how saddlepoint approximation in such models can yield highly accurate quantiles for posterior distributions, and illustrate this numerically, using wavelet regression with point mass/Laplace and point mass/normal prior distributions.
Key Words: Bayesian inference • Median • Mixture distribution • Quantile estimation • Saddlepoint approximation • Spike-and-slab model • Wavelets
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