Statistical Neuroscience

Catalog description

An introduction to the statistical modeling of multiscale neural dynamics in networks of neurons and large-scale brain networks with a focus on stochastic processes and random dynamical systems. Analysis of dynamical and statistical network properties: stationarity, directed transfer functions, stability and bifurcations, phase transitions. Related applications to prediction, control, low-dimensional representation, probabilistic neural population encoding and decoding are introduced as well. This is a course for senior undergraduate and graduate students with a background in systems/computational neuroscience and/or applied math/biomedical engineering. Lectures are accompanied by hands-on Python/Matlab-based applications to real and simulated neural data. Topics include: (1) Time and spectral domain models of network dynamics based on multivariate neural time series and point process observations with exogenous inputs; vector autoregressive processes, nonlinear Hawkes processes; stability, transfer functions; (2) Identification of directed interactions in networks of neurons and brain inter-areal communication (Granger causality, transfer entropy, ODE networks); (3) Collective dynamics and low-dimensional representations of network dynamics; (4) Prediction, neural population encoding and decoding for brain-computer interfaces: Bayesian probabilistic approaches based on linear/nonlinear state-space models, machine learning; (5) Data assimilation methods for modeling neural network dynamics. Example datasets include neuronal spike trains, local field potentials, ECoG/SEEG. PREREQUISITES: Introduction to statistics and probability, calculus and linear algebra; Python/Matlab programming language; familiarity with stochastic processes, difference/differential equations and related math background is helpful. Instructor permission required.