  We propose an evolutionary state space model (E-SSM) for analyzing high
dimensional brain signals whose statistical properties evolve over the course
of a non-spatial memory experiment. Under E-SSM, brain signals are modeled as
mixtures of components (e.g., AR(2) process) with oscillatory activity at
pre-defined frequency bands. To account for the potential non-stationarity of
these components (since the brain responses could vary throughout the entire
experiment), the parameters are allowed to vary over epochs. Compared with
classical approaches such as independent component analysis and filtering, the
proposed method accounts for the entire temporal correlation of the components
and accommodates non-stationarity. For inference purpose, we propose a novel
computational algorithm based upon using Kalman smoother, maximum likelihood
and blocked resampling. The E-SSM model is applied to simulation studies and an
application to a multi-epoch local field potentials (LFP) signal data collected
from a non-spatial (olfactory) sequence memory task study. The results confirm
that our method captures the evolution of the power for different components
across different phases in the experiment and identifies clusters of electrodes
that behave similarly with respect to the decomposition of different sources.
These findings suggest that the activity of different electrodes does change
over the course of an experiment in practice, treating these epoch recordings
as realizations of an identical process could lead to misleading results. In
summary, the proposed method underscores the importance of capturing the
evolution in brain responses over the study period.
