  This paper illustrates novel methods for nonstationary time series modeling
along with their applications to selected problems in neuroscience. These
methods are semi-parametric in that inferences are derived by combining
sequential Bayesian updating with a non-parametric change-point test. As a test
statistic, we propose a Kullback--Leibler (KL) divergence between posterior
distributions arising from different sets of data. A closed form expression of
this statistic is derived for exponential family models, whereas standard
Markov chain Monte Carlo output is used to approximate its value and its
critical region for more general models. The behavior of one-step ahead
predictive distributions under our semi-parametric framework is described
analytically for a dynamic linear time series model. Conditions under which our
approach reduces to fully parametric state-space modeling are also illustrated.
We apply our methods to estimating the functional dynamics of a wide range of
neural data, including multi-channel electroencephalogram recordings,
longitudinal behavioral experiments and in-vivo multiple spike trains
recordings. The estimated dynamics are related to the presentation of visual
stimuli, to the evaluation of a learning performance and to changes in the
functional connections between neurons over a sequence of experiments.
