Semi-parametric dynamic time series modelling with applications to detecting neural dynamics
Rigat, Fabio, 1975- and Smith, J. Q., 1953- (2007) Semi-parametric dynamic time series modelling with applications to detecting neural dynamics. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers, Vol.2007).
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This paper illustrates the theory and applications of a methodology for non-stationary time series modeling which combines sequential parametric Bayesian estimation with non-parametric change-point testing. A novel Kullback-Leibler divergence between posterior distributions arising from different sets of data is proposed as a nonparametric test statistic. A closed form expression of this test statistic is derived for exponential family models whereas Markov chain Monte Carlo simulation is used in general to approximate its value and that of its critical region. The effects of detecting a change-point using our method are assessed analytically for the one-step ahead predictive distribution of a linear dynamic Gaussian time series model. Conditions under which our approach reduces to fully parametric state-space modeling are illustrated. The method is applied to estimating the functional dynamics of a wide range of neural data, including multi-channel electroencephalogram recordings, the learning performance in longitudinal behavioural experiments and in-vivo multiple spike trains. The estimated dynamics are related to the presentation of visual stimuli, to the generation of motor responses and to variations of the functional connections between neurons across different experiments.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Time-series analysis, Change-point problems, Neurons -- Mathematical models|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||32|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||University of Warwick. Centre for Research in Statistical Methodology|
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