Search results for "Multivariate statistics"
showing 10 items of 290 documents
Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis
2011
This tutorial paper introduces a common framework for the evaluation of widely used frequency-domain measures of coupling (coherence, partial coherence) and causality (directed coherence, partial directed coherence) from the parametric representation of linear multivariate (MV) processes. After providing a comprehensive time-domain definition of the various forms of connectivity observed in MV processes, we particularize them to MV autoregressive (MVAR) processes and derive the corresponding frequency-domain measures. Then, we discuss the theoretical interpretation of these MVAR-based connectivity measures, showing that each of them reflects a specific time-domain connectivity definition an…
The multivariate physical activity signature associated with metabolic health in children and youth: An International Children's Accelerometry Databa…
2020
There is solid evidence for an association between physical activity and metabolic health outcomes in children and youth, but for methodological reasons most studies describe the intensity spectrum using only a few summary measures. We aimed to determine the multivariate physical activity intensity signature associated with metabolic health in a large and diverse sample of children and youth, by investigating the association pattern for the entire physical intensity spectrum. We used pooled data from 11 studies and 11,853 participants aged 5.8–18.4 years included in the International Children's Accelerometry Database. We derived 14 accelerometry-derived (ActiGraph) physical activity variabl…
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).
Digital simulation of multivariate earthquake ground motions
2000
In this paper a new generation procedure of multivariate earthquake ground motion is presented. The technique takes full advantage of the decomposition of the power spectral density matrix by means of its eigenvectors. The application of the method to multivariate ground accelerations shows some very interesting physical properties which allows one to obtain significant reduction of the computational effort in the generation of sample functions relative to multivariate earthquake ground motion processes. Copyright © 2000 John Wiley & Sons, Ltd.
Decomposing the transfer entropy to quantify lag-specific Granger causality in cardiovascular variability.
2013
We present a modification of the well known transfer entropy (TE) which makes it able to detect, besides the direction and strength of the information transfer between coupled processes, its exact timing. The approach follows a decomposition strategy which identifies--according to a lag-specific formulation of the concept of Granger causality--the set of time delays carrying significant information, and then assigns to each of these delays an amount of information transfer such that the total contribution yields the overall TE. We propose also a procedure for the practical estimation from time series data of the relevant delays and lag-specific TE in both bivariate and multivariate settings…
Kernel intensity for space-time point processes with application to seismological problems
2010
Dealing with data coming from a space-time inhomogeneous process, there is often the need of semi-parametric estimates of the conditional intensity function; isotropic or anisotropic multivariate kernel estimates can be used, with windows sizes h. The properties of the intensities estimated with this choice of h are not always good for specific fields of application; we could try to choose h in order to have good predictive properties of the estimated intensity function. Since a direct ML approach cannot be followed, we propose an estimation procedure, computationally intensive, based on the subsequent increments of likelihood obtained adding an observation at time. The first results obtain…
Stochastic Nonlinear Time Series Forecasting Using Time-Delay Reservoir Computers: Performance and Universality
2014
International audience; Reservoir computing is a recently introduced machine learning paradigm that has already shown excellent performances in the processing of empirical data. We study a particular kind of reservoir computers called time-delay reservoirs that are constructed out of the sampling of the solution of a time-delay diFFerential equation and show their good performance in the forecasting of the conditional covariances associated to multivariate discrete-time nonlinear stochastic processes of VEC-GARCH type as well as in the prediction of factual daily market realized volatilities computed with intraday quotes, using as training input daily log-return series of moderate size. We …
Forecasting correlated time series with exponential smoothing models
2011
Abstract This paper presents the Bayesian analysis of a general multivariate exponential smoothing model that allows us to forecast time series jointly, subject to correlated random disturbances. The general multivariate model, which can be formulated as a seemingly unrelated regression model, includes the previously studied homogeneous multivariate Holt-Winters’ model as a special case when all of the univariate series share a common structure. MCMC simulation techniques are required in order to approach the non-analytically tractable posterior distribution of the model parameters. The predictive distribution is then estimated using Monte Carlo integration. A Bayesian model selection crite…
Multivariate stochastic wave generation
1996
Abstract In this paper, for the case of the fluid particle velocity, a procedure that substantially reduces the computational effort to generate a multivariate stochastic process is proposed. It is shown that, for a fully coherent wave field, it is possible to decompose the Power Spectral Density (PSD) matrix into the eigenvectors of the matrix itself. This leads to generate each field's process as independent, and the time generation increases linearly with the processes' number in the field. A numerical example to evaluate the statistical properties, in terms of correlation and cross-correlation functions, of the processes is also presented.
Multivariate regression analysis applied to the calibration of equipment used in pig meat classification in Romania.
2016
This paper highlights the statistical methodology used in a dissection experiment carried out in Romania to calibrate and standardize two classification devices, OptiGrade PRO (OGP) and Fat-o-Meat'er (FOM). One hundred forty-five carcasses were measured using the two probes and dissected according to the European reference method. To derive prediction formulas for each device, multiple linear regression analysis was performed on the relationship between the reference lean meat percentage and the back fat and muscle thicknesses, using the ordinary least squares technique. The root mean squared error of prediction calculated using the leave-one-out cross validation met European Commission (EC…