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This paper illustrates novel methods for nonstationary time series modelingalong with their applications to selected problems in neuroscience. Thesemethods are semi-parametric in that inferences are derived by combiningsequential Bayesian updating with a non-parametric change-point test. As a teststatistic, we propose a Kullback--Leibler (KL) divergence between posteriordistributions arising from different sets of data. A closed form expression ofthis statistic is derived for exponential family models, whereas standardMarkov chain Monte Carlo output is used to approximate its value and itscritical region for more general models. The behavior of one-step aheadpredictive distributions under our semi-parametric framework is describedanalytically for a dynamic linear time series model. Conditions under which ourapproach reduces to fully parametric state-space modeling are also illustrated.We apply our methods to estimating the functional dynamics of a wide range ofneural data, including multi-channel electroencephalogram recordings,longitudinal behavioral experiments and in-vivo multiple spike trainsrecordings. The estimated dynamics are related to the presentation of visualstimuli, to the evaluation of a learning performance and to changes in thefunctional connections between neurons over a sequence of experiments.

Semi-parametric dynamic time series modelling with applications to detecting neural dynamics