128,478 research outputs found
Bayesian non-linear large scale structure inference of the Sloan Digital Sky Survey data release 7
In this work we present the first non-linear, non-Gaussian full Bayesian
large scale structure analysis of the cosmic density field conducted so far.
The density inference is based on the Sloan Digital Sky Survey data release 7,
which covers the northern galactic cap. We employ a novel Bayesian sampling
algorithm, which enables us to explore the extremely high dimensional
non-Gaussian, non-linear log-normal Poissonian posterior of the three
dimensional density field conditional on the data. These techniques are
efficiently implemented in the HADES computer algorithm and permit the precise
recovery of poorly sampled objects and non-linear density fields. The
non-linear density inference is performed on a 750 Mpc cube with roughly 3 Mpc
grid-resolution, while accounting for systematic effects, introduced by survey
geometry and selection function of the SDSS, and the correct treatment of a
Poissonian shot noise contribution. Our high resolution results represent
remarkably well the cosmic web structure of the cosmic density field.
Filaments, voids and clusters are clearly visible. Further, we also conduct a
dynamical web classification, and estimated the web type posterior distribution
conditional on the SDSS data.Comment: 18 pages, 11 figure
Combining local regularity estimation and total variation optimization for scale-free texture segmentation
Texture segmentation constitutes a standard image processing task, crucial to
many applications. The present contribution focuses on the particular subset of
scale-free textures and its originality resides in the combination of three key
ingredients: First, texture characterization relies on the concept of local
regularity ; Second, estimation of local regularity is based on new multiscale
quantities referred to as wavelet leaders ; Third, segmentation from local
regularity faces a fundamental bias variance trade-off: In nature, local
regularity estimation shows high variability that impairs the detection of
changes, while a posteriori smoothing of regularity estimates precludes from
locating correctly changes. Instead, the present contribution proposes several
variational problem formulations based on total variation and proximal
resolutions that effectively circumvent this trade-off. Estimation and
segmentation performance for the proposed procedures are quantified and
compared on synthetic as well as on real-world textures
On boosting kernel regression
In this paper we propose a simple multistep regression smoother which is constructed in an iterative manner, by learning the Nadaraya-Watson estimator with L-2 boosting. We find, in both theoretical analysis and simulation experiments, that the bias converges exponentially fast. and the variance diverges exponentially slow. The first boosting step is analysed in more detail, giving asymptotic expressions as functions of the smoothing parameter, and relationships with previous work are explored. Practical performance is illustrated by both simulated and real data
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