Estimation of time-variant, multivariate AR-models with application to interaction analysis in the human brain
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1
Friedrich Schiller University , Institute of Medical Statistics Computer Sciences and Documentation, Germany
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2
Friedrich Schiller University Jena, Department of Psychology, Germany
Aim:In this Study, a new Kalman-Filter approach is presented for the estimation of high dimensional time variant multivariate AR-processes.
Methods: Firstly, the new Kalman filter algorithm and an ERP dataset derived from an experiment with noxious laser stimuli are presented. To validate the possibilities of the new method, the Kalman filter and the RLS algorithm with forgetting factor are compared with regard to their applicability to high-dimensional time series. In order to test both approaches simulated and measured time series were used. In a multi-trial approach directed interactions between event-related potentials (ERPs) were computed. The time-variant Granger Causality Index was used for interaction analysis.
Results: It can be shown that the Kalman approach enables a time-variant parameter estimation of a 58-dimensional multivariate AR model. The RLS-based algorithm fails for dimensions higher than . The interaction analysis on the simulated data-set shows, that the Kalman-filter produces more reliable time-variant granger causality indices than the RLS. Conclusion: The high-dimensional AR model provides an improved neurophysiological interpretation of the computed interaction networks. Kalman filter based algorithms are applicable for such high-dimensional analysis. One of the advantages of the Kalman filter based algorithms is the multiplicity to design the course of the estimated time-variant AR-parameters. This is impossible with just one single forgetting factor like RLS provides.
Acknowledgments: This study was in part supported by the Federal Ministry of Education and Research (Bernstein Group, 01GQ0703; application), the German Research Council (DFG Wi 1166/9-1 Gamma; method's development) and the COST Action BM0601 NEUROMATH.
Conference:
NeuroMath COST Action BM0601: Neurodynamic Insight into Functional Connectivity, Cognition, and Consciousness, Dubrovnik, Croatia, 27 Mar - 28 Mar, 2010.
Presentation Type:
Poster Presentation
Topic:
Posters
Citation:
Milde
T,
Leistritz
L,
Weiss
T and
Witte
H
(2010). Estimation of time-variant, multivariate AR-models with application to interaction analysis in the human brain.
Front. Neurosci.
Conference Abstract:
NeuroMath COST Action BM0601: Neurodynamic Insight into Functional Connectivity, Cognition, and Consciousness.
doi: 10.3389/conf.fnins.2010.05.00030
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Received:
24 Jul 2010;
Published Online:
24 Jul 2010.
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Correspondence:
Thomas Milde, Friedrich Schiller University, Institute of Medical Statistics Computer Sciences and Documentation, Jena, Germany, thomas.milde@mti.uni-jena.de