%0 Journal Article %1 SylVainReguarlisedMRF2004 %A Sardy, Sylvain %A Tseng, Paul %D 2004 %I American Statistical Association %J Journal of the American Statistical Association %K Bayes assimilation bayes bayesian datassimilation imageprocessing inference markovrandomfields regularization statistics uncertainty %N 465 %P 191--204 %T On the Statistical Analysis of Smoothing by Maximizing Dirty Markov Random Field Posterior Distributions %U http://www.jstor.org/stable/27590365 %V 99 %X We consider Bayesian nonparametric function estimation using a Markov random field prior based on the Laplace distribution. We describe efficient methods for finding the exact maximum a posteriori estimate, which handle constraints naturally and avoid the problems posed by nondifferentiability of the posterior distribution; the methods also make links to spline and wavelet smoothers and to a dual posterior distribution. Three automatic smoothing parameter selection procedures are described: empirical Bayes, two-fold cross-validation, and a universal rule for the Laplace prior. Monte Carlo simulation with Gaussian and Poisson responses demonstrates that the new estimator can give better estimates of nonsmooth functions than can a similar prior based on the Gaussian distribution or wavelet-based competitors. Applications are given to spectral density estimation and to Poisson image denoising.

@article{SylVainReguarlisedMRF2004, abstract = {We consider Bayesian nonparametric function estimation using a Markov random field prior based on the Laplace distribution. We describe efficient methods for finding the exact maximum a posteriori estimate, which handle constraints naturally and avoid the problems posed by nondifferentiability of the posterior distribution; the methods also make links to spline and wavelet smoothers and to a dual posterior distribution. Three automatic smoothing parameter selection procedures are described: empirical Bayes, two-fold cross-validation, and a universal rule for the Laplace prior. Monte Carlo simulation with Gaussian and Poisson responses demonstrates that the new estimator can give better estimates of nonsmooth functions than can a similar prior based on the Gaussian distribution or wavelet-based competitors. Applications are given to spectral density estimation and to Poisson image denoising.}, added-at = {2010-02-02T20:53:59.000+0100}, author = {Sardy, Sylvain and Tseng, Paul}, biburl = {https://www.bibsonomy.org/bibtex/2269dac8f2534f154257439679fb2f64c/jgomezdans}, copyright = {Copyright © 2004 American Statistical Association}, interhash = {6c6735504e36bb9b2d6e3169cac52065}, intrahash = {269dac8f2534f154257439679fb2f64c}, issn = {01621459}, journal = {Journal of the American Statistical Association}, jstor_articletype = {primary_article}, jstor_formatteddate = {Mar., 2004}, keywords = {Bayes assimilation bayes bayesian datassimilation imageprocessing inference markovrandomfields regularization statistics uncertainty}, number = 465, pages = {191--204}, publisher = {American Statistical Association}, timestamp = {2010-02-02T20:53:59.000+0100}, title = {On the Statistical Analysis of Smoothing by Maximizing Dirty Markov Random Field Posterior Distributions}, url = {http://www.jstor.org/stable/27590365}, volume = 99, year = 2004 }