Rigat, Fabio and Smith, J. Q. (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 (No.7).

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Abstract

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, Engineering and Medicine > 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
Official Date:	2007
Dates:	Date Event 2007 Published
Volume:	Vol.2007
Number:	No.7
Number of Pages:	32
Institution:	University of Warwick
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	1 August 2016
Date of first compliant Open Access:	1 August 2016
Funder:	University of Warwick. Centre for Research in Statistical Methodology

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