Search results for "Probability Distribution"
showing 10 items of 263 documents
Embedding Quantum into Classical: Contextualization vs Conditionalization
2014
We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is "automatically" labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type ine…
MuTE: a MATLAB toolbox to compare established and novel estimators of the multivariate transfer entropy.
2014
A challenge for physiologists and neuroscientists is to map information transfer between components of the systems that they study at different scales, in order to derive important knowledge on structure and function from the analysis of the recorded dynamics. The components of physiological networks often interact in a nonlinear way and through mechanisms which are in general not completely known. It is then safer that the method of choice for analyzing these interactions does not rely on any model or assumption on the nature of the data and their interactions. Transfer entropy has emerged as a powerful tool to quantify directed dynamical interactions. In this paper we compare different ap…
Second-order interaction in a Trivariate Generalized Gamma Distribution
2004
The concept of second- (and higher-) order interaction is widely used in categorical data analysis, where it proves useful for explaining the interdependence among three (or more) variables. Its use seems to be less common for continuous multivariate distributions, most likely owing to the predominant role of the Multivariate Normal distribution, for which any interaction involving more than two variables is necessarily zero. In this paper we explore the usefulness of a second-order interaction measure for studying the interdependence among three continuous random variables, by applying it to a trivariate Generalized Gamma distribution proposed by Bologna(2000).
Non-Parametric Rank Statistics for Spectral Power and Coherence
2019
AbstractDespite advances in multivariate spectral analysis of neural signals, the statistical inference of measures such as spectral power and coherence in practical and real-life scenarios remains a challenge. The non-normal distribution of the neural signals and presence of artefactual components make it difficult to use the parametric methods for robust estimation of measures or to infer the presence of specific spectral components above the chance level. Furthermore, the bias of the coherence measures and their complex statistical distributions are impediments in robust statistical comparisons between 2 different levels of coherence. Non-parametric methods based on the median of auto-/c…
640-Slice CT Measurement of Superior Orbital Fissure as Gateway for Light into the Brain: Statistical Evaluation of Area and Distance.
2016
Objective Our aim was to provide normative data concerning superior orbital fissure area (SOFA), ocular skin and the substantia nigra (D-SS) and orbital fissure and the substantia nigra (D-SOF-S) distances by CT scan in adult Caucasian population. Methods The area of the superior orbital fissure (SOF), the distance between the ocular skin and the substantia nigra and the distance between the superior orbital fissure and the substantia nigra using CT and 3D-CT images. Results Normative data stratified for age and gender were obtained. The data here reported show that some degree of variability in SOFA, D-SS and D-SOF-S measurements can be observed healthy Caucasian subjects. Gender stratifie…
Infinitely Divisible Distributions
2020
For every n, the normal distribution with expectation μ and variance σ 2 is the nth convolution power of a probability measure (namely of the normal distribution with expectation μ/n and variance σ 2/n). This property is called infinite divisibility and is shared by other probability distributions such as the Poisson distribution and the Gamma distribution. In the first section, we study which probability measures on the real line are infinitely divisible and give an exhaustive description of this class of distributions by means of the Levy–Khinchin formula.
Brief Introduction to Probability Distributions
2014
There is a great deal of uncertainty in any project. That is, data is seldom absolutely reliable and exact, since there is never certainty about duration of tasks, price variations, effect on the environment, etc., to say nothing about those aspects which are external to the project and for which the project developer has no control, such as weather conditions, demand, stock fluctuations, inflation, supplier’s delays, etc. It is believed that many projects are not completed in time and finish with cost overrun, because in their preparation, data is taken as unquestionable, and then actual conditions show that it is not precisely the case. For this reason the uncertainty aspect has to be con…
Probabilities in Risk Management
2014
A project is generally a complex undertaking in which most things are uncertain (durations, costs, project and suppliers performance, weather, soil geology, public reaction, etc.), and thus, risk permeates everything. Risk is closely related to uncertainty, and the latter with probabilities and distributions the conceptual aspects of which are explained in Chap. 9. It is inconceivable to address risk without considering probabilities of occurrence, and the measures that must be taken to prevent or mitigate risk; in that sense, the ‘buffer’ concept is introduced. In Chap. 2, a comparison was mentioned between CPM, PERT and MC; now, Chap. 3 proposes a case for numerically demonstrating the ad…
A novel method based on augmented Markov vector process for the time-variant extreme value distribution of stochastic dynamical systems enforced by P…
2020
Abstract The probability density function (PDF) of the time-variant extreme value process for structural responses is of great importance. Poisson white noise excitation occurs widely in practical engineering problems. The extreme value distribution of the response of systems excited by Poisson white noise processes is still not yet readily available. For this purpose, in the present paper, a novel method based on the augmented Markov vector process for the PDF of the time-variant extreme value process for a Poisson white noise driven dynamical system is proposed. Specifically, the augmented Markov vector (AMV) process is constructed by combining the extreme value process and its underlying…
Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach
2015
Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computation…