Search results for " Statistics and Probability"
showing 10 items of 117 documents
Multiscale analysis of information dynamics for linear multivariate processes.
2016
In the study of complex physical and physiological systems represented by multivariate time series, an issue of great interest is the description of the system dynamics over a range of different temporal scales. While information-theoretic approaches to the multiscale analysis of complex dynamics are being increasingly used, the theoretical properties of the applied measures are poorly understood. This study introduces for the first time a framework for the analytical computation of information dynamics for linear multivariate stochastic processes explored at different time scales. After showing that the multiscale processing of a vector autoregressive (VAR) process introduces a moving aver…
Gradients of O-information: Low-order descriptors of high-order dependencies
2023
O-information is an information-theoretic metric that captures the overall balance between redundant and synergistic information shared by groups of three or more variables. To complement the global assessment provided by this metric, here we propose the gradients of the O-information as low-order descriptors that can characterise how high-order effects are localised across a system of interest. We illustrate the capabilities of the proposed framework by revealing the role of specific spins in Ising models with frustration, and on practical data analysis on US macroeconomic data. Our theoretical and empirical analyses demonstrate the potential of these gradients to highlight the contributio…
Simulation-based marginal likelihood for cluster strong lensing cosmology
2015
Comparisons between observed and predicted strong lensing properties of galaxy clusters have been routinely used to claim either tension or consistency with $\Lambda$CDM cosmology. However, standard approaches to such cosmological tests are unable to quantify the preference for one cosmology over another. We advocate approximating the relevant Bayes factor using a marginal likelihood that is based on the following summary statistic: the posterior probability distribution function for the parameters of the scaling relation between Einstein radii and cluster mass, $\alpha$ and $\beta$. We demonstrate, for the first time, a method of estimating the marginal likelihood using the X-ray selected …
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…
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…
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…
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.
Multimodal and multicriteria analysis for VLSI expertises and defects localization
2017
The purpose of this manuscript is to exhibit the research work solving the issue of data processing stem from defect localization techniques. This step being decisive in the failure analysis process, scientists have to harness data coming from light emission and laser techniques. Nevertheless, this analysis process is sequential and only depends on the expert’s decision. This factor leads to a not quantified probability of localization. Consequently to solve these issues, a multimodal and multicriteria analysis has been developped, taking advantage of the heterogeneous andcomplementary nature of light emission and laser probing techniques. This kind of process is based on advanced level too…
An update on nuclear PDFs at the LHeC
2017
The prospects for a measurement of nuclear parton distribution functions (PDFs) at the Large Hadron--Electron Collider are discussed in the light of recent progress made in the front of global analysis of nuclear PDFs.
"Table 3" of "Spin asymmetries A(1) and structure functions g1 of the proton and the deuteron from polarized high energy muon scattering."
1998
The virtual photon proton asymmetries in smaller X and Q**2 bins. bins. Errors are statistical only.