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Evolutionary state-space model and its application to time-frequency analysis of local field potentials. (English) Zbl 1453.62724

Summary: We propose an evolutionary state-space model (E-SSM) for analyzing high-dimensional brain signals, the statistical properties of which evolve over the course of a nonspatial memory experiment. Under the E-SSM, brain signals are modeled as mixtures of components (e.g., an AR(2) process) with oscillatory activity at predefined frequency bands. To account for the potential nonstationarity of these components (because brain responses can vary throughout an experiment), the parameters are allowed to vary over epochs. Compared with classical approaches, such as independent component analyses and filtering, the proposed method accounts for the entire temporal correlation of the components and accommodates nonstationarity. For inference purposes, we propose a novel computational algorithm based on a Kalman smoother, maximum likelihood, and blocked resampling. The E-SSM model is applied in simulation studies and applied to multi-epoch local field potential (LFP) signal data, collected from a nonspatial (olfactory) sequence memory task study. The results confirm that our method captures the evolution of the power of the 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 electrodes does change over the course of an experiment in practice. Thus, 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.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62M15 Inference from stochastic processes and spectral analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Software:

astsa; EEGLAB; HIBITS; HINT
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References:

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[32] Department of Statistics, University of California, Irvine, 2226 Donald Bren Hall, Irvine, CA
[33] 92697-1250, USA.
[34] E-mail: xgao2@uci.edu
[35] Department of Statistics, University of California, Irvine, 2206 Donald Bren Hall, Irvine, CA
[36] 92697-1250, USA.
[37] E-mail: weinings@uci.edu
[38] Department of Statistics, University of California, Irvine, 2224 Donald Bren Hall, Irvine, CA
[39] 92697-1250, USA.
[40] E-mail: babaks@uci.edu
[41] University of California, Irvine, 106 Bonney Research Laboratory Building Department of Neu
[42] robiology and Behavior, Irvine, CA 92697, USA.
[43] E-mail: norbert.fortin@uci.edu
[44] Statistics Program, 4700 King Abdullah University of Science and Technology (KAUST) Thuwal,
[45] 23955-6900, Kingdom of Saudi Arabia, USA.
[46] E-mail: hernando.
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