5,939 research outputs found
Adaptive Langevin Sampler for Separation of t-Distribution Modelled Astrophysical Maps
We propose to model the image differentials of astrophysical source maps by
Student's t-distribution and to use them in the Bayesian source separation
method as priors. We introduce an efficient Markov Chain Monte Carlo (MCMC)
sampling scheme to unmix the astrophysical sources and describe the derivation
details. In this scheme, we use the Langevin stochastic equation for
transitions, which enables parallel drawing of random samples from the
posterior, and reduces the computation time significantly (by two orders of
magnitude). In addition, Student's t-distribution parameters are updated
throughout the iterations. The results on astrophysical source separation are
assessed with two performance criteria defined in the pixel and the frequency
domains.Comment: 12 pages, 6 figure
Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
Structured additive regression provides a general framework for complex
Gaussian and non-Gaussian regression models, with predictors comprising
arbitrary combinations of nonlinear functions and surfaces, spatial effects,
varying coefficients, random effects and further regression terms. The large
flexibility of structured additive regression makes function selection a
challenging and important task, aiming at (1) selecting the relevant
covariates, (2) choosing an appropriate and parsimonious representation of the
impact of covariates on the predictor and (3) determining the required
interactions. We propose a spike-and-slab prior structure for function
selection that allows to include or exclude single coefficients as well as
blocks of coefficients representing specific model terms. A novel
multiplicative parameter expansion is required to obtain good mixing and
convergence properties in a Markov chain Monte Carlo simulation approach and is
shown to induce desirable shrinkage properties. In simulation studies and with
(real) benchmark classification data, we investigate sensitivity to
hyperparameter settings and compare performance to competitors. The flexibility
and applicability of our approach are demonstrated in an additive piecewise
exponential model with time-varying effects for right-censored survival times
of intensive care patients with sepsis. Geoadditive and additive mixed logit
model applications are discussed in an extensive appendix
Posterior Mean Super-Resolution with a Compound Gaussian Markov Random Field Prior
This manuscript proposes a posterior mean (PM) super-resolution (SR) method
with a compound Gaussian Markov random field (MRF) prior. SR is a technique to
estimate a spatially high-resolution image from observed multiple
low-resolution images. A compound Gaussian MRF model provides a preferable
prior for natural images that preserves edges. PM is the optimal estimator for
the objective function of peak signal-to-noise ratio (PSNR). This estimator is
numerically determined by using variational Bayes (VB). We then solve the
conjugate prior problem on VB and the exponential-order calculation cost
problem of a compound Gaussian MRF prior with simple Taylor approximations. In
experiments, the proposed method roughly overcomes existing methods.Comment: 5 pages, 20 figures, 1 tables, accepted to ICASSP2012 (corrected
2012/3/23
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