19,926 research outputs found

    Stability

    Full text link
    Reproducibility is imperative for any scientific discovery. More often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical results relative to "reasonable" perturbations to data and to the model used. Jacknife, bootstrap, and cross-validation are based on perturbations to data, while robust statistics methods deal with perturbations to models. In this article, a case is made for the importance of stability in statistics. Firstly, we motivate the necessity of stability for interpretable and reliable encoding models from brain fMRI signals. Secondly, we find strong evidence in the literature to demonstrate the central role of stability in statistical inference, such as sensitivity analysis and effect detection. Thirdly, a smoothing parameter selector based on estimation stability (ES), ES-CV, is proposed for Lasso, in order to bring stability to bear on cross-validation (CV). ES-CV is then utilized in the encoding models to reduce the number of predictors by 60% with almost no loss (1.3%) of prediction performance across over 2,000 voxels. Last, a novel "stability" argument is seen to drive new results that shed light on the intriguing interactions between sample to sample variability and heavier tail error distribution (e.g., double-exponential) in high-dimensional regression models with pp predictors and nn independent samples. In particular, when p/nκ(0.3,1)p/n\rightarrow\kappa\in(0.3,1) and the error distribution is double-exponential, the Ordinary Least Squares (OLS) is a better estimator than the Least Absolute Deviation (LAD) estimator.Comment: Published in at http://dx.doi.org/10.3150/13-BEJSP14 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

    Detecting Unspecified Structure in Low-Count Images

    Full text link
    Unexpected structure in images of astronomical sources often presents itself upon visual inspection of the image, but such apparent structure may either correspond to true features in the source or be due to noise in the data. This paper presents a method for testing whether inferred structure in an image with Poisson noise represents a significant departure from a baseline (null) model of the image. To infer image structure, we conduct a Bayesian analysis of a full model that uses a multiscale component to allow flexible departures from the posited null model. As a test statistic, we use a tail probability of the posterior distribution under the full model. This choice of test statistic allows us to estimate a computationally efficient upper bound on a p-value that enables us to draw strong conclusions even when there are limited computational resources that can be devoted to simulations under the null model. We demonstrate the statistical performance of our method on simulated images. Applying our method to an X-ray image of the quasar 0730+257, we find significant evidence against the null model of a single point source and uniform background, lending support to the claim of an X-ray jet

    Searching dark-matter halos in the GaBoDS survey

    Get PDF
    We apply the linear filter for the weak-lensing signal of dark-matter halos developed in Maturi et al. (2005) to the cosmic-shear data extracted from the Garching-Bonn-Deep-Survey (GaBoDS). We wish to search for dark-matter halos through weak-lensing signatures which are significantly above the random and systematic noise level caused by intervening large-scale structures. We employ a linear matched filter which maximises the signal-to-noise ratio by minimising the number of spurious detections caused by the superposition of large-scale structures (LSS). This is achieved by suppressing those spatial frequencies dominated by the LSS contamination. We confirm the improved stability and reliability of the detections achieved with our new filter compared to the commonly-used aperture mass (Schneider, 1996; Schneider et al., 1998) and to the aperture mass based on the shear profile expected for NFW haloes (see e.g. Schirmer et al., 2004; Hennawi & Spergel, 2005). Schirmer et al.~(2006) achieved results comparable to our filter, but probably only because of the low average redshift of the background sources in GaBoDS, which keeps the LSS contamination low. For deeper data, the difference will be more important, as shown by Maturi et al. (2005). We detect fourteen halos on about eighteen square degrees selected from the survey. Five are known clusters, two are associated with over-densities of galaxies visible in the GaBoDS image, and seven have no known optical or X-ray counterparts.Comment: 8 pages, 4 figures, accepted by A&

    Segmentation of skin lesions in 2D and 3D ultrasound images using a spatially coherent generalized Rayleigh mixture model

    Get PDF
    This paper addresses the problem of jointly estimating the statistical distribution and segmenting lesions in multiple-tissue high-frequency skin ultrasound images. The distribution of multiple-tissue images is modeled as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by enforcing local dependence between the mixture components. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. More precisely, a hybrid Metropolis-within-Gibbs sampler is used to draw samples that are asymptotically distributed according to the posterior distribution of the Bayesian model. The Bayesian estimators of the model parameters are then computed from the generated samples. Simulation results are conducted on synthetic data to illustrate the performance of the proposed estimation strategy. The method is then successfully applied to the segmentation of in vivo skin tumors in high-frequency 2-D and 3-D ultrasound images
    corecore