13,720 research outputs found
A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?
Predicting historic temperatures based on tree rings, ice cores, and other
natural proxies is a difficult endeavor. The relationship between proxies and
temperature is weak and the number of proxies is far larger than the number of
target data points. Furthermore, the data contain complex spatial and temporal
dependence structures which are not easily captured with simple models. In this
paper, we assess the reliability of such reconstructions and their statistical
significance against various null models. We find that the proxies do not
predict temperature significantly better than random series generated
independently of temperature. Furthermore, various model specifications that
perform similarly at predicting temperature produce extremely different
historical backcasts. Finally, the proxies seem unable to forecast the high
levels of and sharp run-up in temperature in the 1990s either in-sample or from
contiguous holdout blocks, thus casting doubt on their ability to predict such
phenomena if in fact they occurred several hundred years ago. We propose our
own reconstruction of Northern Hemisphere average annual land temperature over
the last millennium, assess its reliability, and compare it to those from the
climate science literature. Our model provides a similar reconstruction but has
much wider standard errors, reflecting the weak signal and large uncertainty
encountered in this setting.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS398 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Gaussian process tomography for soft x-ray spectroscopy at WEST without equilibrium information
International audienceGaussian process tomography (GPT) is a recently developed tomography method based on the Bayesian probability theory [J. Svensson, JET Internal Report EFDA-JET-PR(11)24, 2011 and Li et al., Rev. Sci. Instrum. 84, 083506 (2013)]. By modeling the soft X-ray (SXR) emissivity field in a poloidal cross section as a Gaussian process, the Bayesian SXR tomography can be carried out in a robust and extremely fast way. Owing to the short execution time of the algorithm, GPT is an important candidate for providing real-time reconstructions with a view to impurity transport and fast magnetohydrodynamic control. In addition, the Bayesian formalism allows quantifying uncertainty on the inferred parameters. In this paper, the GPT technique is validated using a synthetic data set expected from the WEST tokamak, and the results are shown of its application to the reconstruction of SXR emissivity profiles measured on Tore Supra. The method is compared with the standard algorithm based on minimization of the Fisher information
A Bayesian Approach to Manifold Topology Reconstruction
In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated
Contour Generator Points for Threshold Selection and a Novel Photo-Consistency Measure for Space Carving
Space carving has emerged as a powerful method for multiview scene reconstruction. Although a wide variety of methods have been proposed, the quality of the reconstruction remains highly-dependent on the photometric consistency measure, and the threshold used to carve away voxels. In this paper, we present a novel photo-consistency measure that is motivated by a multiset variant of the chamfer distance. The new measure is robust to high amounts of within-view color variance and also takes into account the projection angles of back-projected pixels.
Another critical issue in space carving is the selection of the photo-consistency threshold used to determine what surface voxels are kept or carved away. In this paper, a reliable threshold selection technique is proposed that examines the photo-consistency values at contour generator points. Contour generators are points that lie on both the surface of the object and the visual hull. To determine the threshold, a percentile ranking of the photo-consistency values of these generator points is used. This improved technique is applicable to a wide variety of photo-consistency measures, including the new measure presented in this paper. Also presented in this paper is a method to choose between photo-consistency measures, and voxel array resolutions prior to carving using receiver operating characteristic (ROC) curves
Model-Free Multi-Probe Lensing Reconstruction of Cluster Mass Profiles
Lens magnification by galaxy clusters induces characteristic spatial
variations in the number counts of background sources, amplifying their
observed fluxes and expanding the area of sky, the net effect of which, known
as magnification bias, depends on the intrinsic faint-end slope of the source
luminosity function. The bias is strongly negative for red galaxies, dominated
by the geometric area distortion, whereas it is mildly positive for blue
galaxies, enhancing the blue counts toward the cluster center. We generalize
the Bayesian approach of Umetsu et al. for reconstructing projected cluster
mass profiles, by incorporating multiple populations of background sources for
magnification bias measurements and combining them with complementary lens
distortion measurements, effectively breaking the mass-sheet degeneracy and
improving the statistical precision of cluster mass measurements. The approach
can be further extended to include strong-lensing projected mass estimates,
thus allowing for non-parametric absolute mass determinations in both the weak
and strong regimes. We apply this method to our recent CLASH lensing
measurements of MACS J1206.2-0847, and demonstrate how combining multi-probe
lensing constraints can improve the reconstruction of cluster mass profiles.
This method will also be useful for a stacked lensing analysis, combining all
lensing-related effects in the cluster regime, for a definitive determination
of the averaged mass profile.Comment: 13 pages, 2 figures; Typo corrections (Appendix A.2.) to match the
published version in Ap
A stochastic approach to reconstruction of faults in elastic half space
We introduce in this study an algorithm for the imaging of faults and of slip
fields on those faults. The physics of this problem are modeled using the
equations of linear elasticity. We define a regularized functional to be
minimized for building the image. We first prove that the minimum of that
functional converges to the unique solution of the related fault inverse
problem. Due to inherent uncertainties in measurements, rather than seeking a
deterministic solution to the fault inverse problem, we then consider a
Bayesian approach. In this approach the geometry of the fault is assumed to be
planar, it can thus be modeled by a three dimensional random variable whose
probability density has to be determined knowing surface measurements. The
randomness involved in the unknown slip is teased out by assuming independence
of the priors, and we show how the regularized error functional introduced
earlier can be used to recover the probability density of the geometry
parameter. The advantage of the Bayesian approach is that we obtain a way of
quantifying uncertainties as part of our final answer. On the downside, this
approach leads to a very large computation since the slip is unknown. To
contend with the size of this computation we developed an algorithm for the
numerical solution to the stochastic minimization problem which can be easily
implemented on a parallel multi-core platform and we discuss techniques aimed
at saving on computational time. After showing how this algorithm performs on
simulated data, we apply it to measured data. The data was recorded during a
slow slip event in Guerrero, Mexico.Comment: In this new version the second error functional is directly minimized
over a finite dimensional space leading to a more natural connection to the
stochastic formulatio
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