Whitening as a tool for estimating mutual information in spatiotemporal data sets
type: Item
instance of: scholarly article
title: Whitening as a tool for estimating mutual information in spatiotemporal data sets
zbMATH Open document ID: 1108.62090
author: Andreas Galka
author: Tohru Ozaki
author: Jorge Bosch Bayard
author: Okito Yamashita
published in: Journal of Statistical Physics
publication date: 2006-12-19T00:00:00Z
review text: For a pair of time series \(x_t\) and \(y_t\), \(t=1, \dots , N_t\), the authors define the mutual information between \(x\) and \(y\) by \[ I(x,y)=\log p((x_1,y_1),\dots , (x_{N_t},y_{N_t})) - \log(p(x_1,\dots , x_{N_t})p(y_1,\dots , y_{N_t})), \] where \(p\) denotes the corresponding joint distribution, and in the joint distribution of all elements of both time series the elements are ordered as pairs. The aim of the paper is to clarify the relations between predictive modelling, maximum likelihood estimation, model comparison, linear correlation and mutual information. The authors interpret modelling as a process of spatial and temporal whitening of the raw data, i.e., transforming it into spatially and temporally uncorrelated innovations. A parsimonious multivariate autoregressive model based on nearest-neighbour interactions is employed. The paper concentrates on the presentation of the methodology and its theoretical background, assuming just the presence of a spatially extended dynamical system, from which the spatiotemporal data has been recorded. Nevertheless, the authors illustrate the practical applications of the methodology by showing results of analysing simulated data sets generated by a system of coupled stochastic oscillators.
reviewed by: Ryszard Doman
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 62H20
zbMATH DE Number: 5080740
zbMATH Keywords: time series analysis
zbMATH Keywords: innovations
zbMATH Keywords: mutual information
zbMATH Keywords: whitening
zbMATH Keywords: spatiotemporal modelling
describes a project that uses: Flury
describes a project that uses: ARfit
describes a project that uses: FastICA
MaRDI profile type: Publication
full work available at URL: s10955-006-9131-x
OpenAlex ID: W2031586101
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DOI: 10.1007/S10955-006-9131-X
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description: scientific article; zbMATH DE number 5080740