Evolutionary State-Space Model and Its Application to Time-Frequency Analysis of Local Field Potentials

We propose an evolutionary state space model (E-SSM) for analyzing high dimensional brain signals (in particular, local field potentials in rats) whose statistical properties evolve over the course of a non-spatial memory experiment. Under E-SSM, brain signals are modeled as mixtures of components with oscillatory activity at defined frequency bands. One unique feature of E-SSM is that the components are parametrized as second order autoregressive AR(2) processes. To account for the potential nonstationarity of these components (since the brain responses could vary throughout the entire experiment), the parameters are allowed to vary over epochs. In contrast to independent component analysis, the method for estimating the components in E-SSM accounts for the entire temporal correlation of the components. Moreover, compared to purely data-adaptive strategies, such as filtering, E-SSM easily accommodates non-stationarity through the component of AR parameters. To estimate the model parameters and conduct statistical inference, we use Kalman smoother, maximum likelihood and blocked resampling approaches. The E-SSM model is applied to a multi-epoch LFP signals from a rat in a non-spatial (olfactory) sequence memory task. Our method captures the evolution of the power for different components across phases 1 ar X iv :1 61 0. 07 27 1v 2 [ st at .M E ] 2 N ov 2 01 6 of the experiment. The E-SSM model also identifies clusters of electrodes that behave similarly with respect to the decomposition of different sources. These findings suggest that the activity of different electrodes changes over the course of the experiment. Treating these epoch recordings as realizations of an identical process could give rise to misleading results. The proposed model underscores the importance of capturing the evolution in brain responses during the course of an experiment.