Search results for " statistics"
showing 10 items of 1891 documents
Community characterization of heterogeneous complex systems
2011
We introduce an analytical statistical method to characterize the communities detected in heterogeneous complex systems. By posing a suitable null hypothesis, our method makes use of the hypergeometric distribution to assess the probability that a given property is over-expressed in the elements of a community with respect to all the elements of the investigated set. We apply our method to two specific complex networks, namely a network of world movies and a network of physics preprints. The characterization of the elements and of the communities is done in terms of languages and countries for the movie network and of journals and subject categories for papers. We find that our method is ab…
Statistical Performance Analysis of a Fast Super-Resolution Technique Using Noisy Translations.
2014
It is well known that the registration process is a key step for super-resolution reconstruction. In this work, we propose to use a piezoelectric system that is easily adaptable on all microscopes and telescopes for controlling accurately their motion (down to nanometers) and therefore acquiring multiple images of the same scene at different controlled positions. Then a fast super-resolution algorithm \cite{eh01} can be used for efficient super-resolution reconstruction. In this case, the optimal use of $r^2$ images for a resolution enhancement factor $r$ is generally not enough to obtain satisfying results due to the random inaccuracy of the positioning system. Thus we propose to take seve…
Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence
2017
International audience; We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total-variation. Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought. We establish a closed form expression for the one-dimensional case, as well as an upper-bound for the two-dimensional case, that appears reasonably tight in practice. This problem is d…
Synergetic and redundant information flow detected by unnormalized Granger causality: application to resting state fMRI
2015
Objectives: We develop a framework for the analysis of synergy and redundancy in the pattern of information flow between subsystems of a complex network. Methods: The presence of redundancy and/or synergy in multivariate time series data renders difficult to estimate the neat flow of information from each driver variable to a given target. We show that adopting an unnormalized definition of Granger causality one may put in evidence redundant multiplets of variables influencing the target by maximizing the total Granger causality to a given target, over all the possible partitions of the set of driving variables. Consequently we introduce a pairwise index of synergy which is zero when two in…
Bayesian Analysis of Population Health Data
2021
The analysis of population-wide datasets can provide insight on the health status of large populations so that public health officials can make data-driven decisions. The analysis of such datasets often requires highly parameterized models with different types of fixed and random effects to account for risk factors, spatial and temporal variations, multilevel effects and other sources on uncertainty. To illustrate the potential of Bayesian hierarchical models, a dataset of about 500,000 inhabitants released by the Polish National Health Fund containing information about ischemic stroke incidence for a 2-year period is analyzed using different types of models. Spatial logistic regression and…
Fast PET Scan Tumor Segmentation Using Superpixels, Principal Component Analysis and K-Means Clustering
2018
Positron Emission Tomography scan images are extensively used in radiotherapy planning, clinical diagnosis, assessment of growth and treatment of a tumor. These all rely on fidelity and speed of detection and delineation algorithm. Despite intensive research, segmentation remained a challenging problem due to the diverse image content, resolution, shape, and noise. This paper presents a fast positron emission tomography tumor segmentation method in which superpixels are extracted first from the input image. Principal component analysis is then applied on the superpixels and also on their average. Distance vector of each superpixel from the average is computed in principal components coordin…
General framework for testing Poisson-Voronoi assumption for real microstructures
2020
Modeling microstructures is an interesting problem not just in Materials Science but also in Mathematics and Statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single phase steel microstructures. The aim of this paper is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of 2D sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, thre…
Can visualization alleviate dichotomous thinking? Effects of visual representations on the cliff effect
2021
Common reporting styles for statistical results in scientific articles, such as $p$ p -values and confidence intervals (CI), have been reported to be prone to dichotomous interpretations, especially with respect to the null hypothesis significance testing framework. For example when the $p$ p -value is small enough or the CIs of the mean effects of a studied drug and a placebo are not overlapping, scientists tend to claim significant differences while often disregarding the magnitudes and absolute differences in the effect sizes. This type of reasoning has been shown to be potentially harmful to science. Techniques relying on the visual estimation of the strength of evidence have been recom…
The limit order book on different time scales
2007
Financial markets can be described on several time scales. We use data from the limit order book of the London Stock Exchange (LSE) to compare how the fluctuation dominated microstructure crosses over to a more systematic global behavior.
LAMN in a class of parametric models for null recurrent diffusion
2017
We study statistical models for one-dimensional diffusions which are recurrent null. A first parameter in the drift is the principal one, and determines regular varying rates of convergence for the score and the information process. A finite number of other parameters, of secondary importance, introduces additional flexibility for the modelization of the drift, and does not perturb the null recurrent behaviour. Under time-continuous observation we obtain local asymptotic mixed normality (LAMN), state a local asymptotic minimax bound, and specify asymptotically optimal estimators.