Statistical measures for neural data analysis

The advent of modern recording methods has led to an explosion of neural data collected from animal and human brains. One challenge for modern neuroscience is the development of a variety of statistical methods for the analysis of neural time series data. I am interested in developing multivariate spectral analysis tools that can be used to analyze and interpret the temporal correlation structure of neuronal activity. Particularly, we are interested in the role of oscillations as a neural code. Several cortical regions show a clear increase in oscillations in the local field potential (a measure of synchronous synaptic activity over a region that includes thousands of neurons) during a behaviorally relevant event. Moreover, single neuron activity also shows temporal structure, with spikes locked to particular phases of the local field oscillation. We are interested in adapting techniques from nonlinear dynamics, information theory, spectral analysis and geophysics to analyze continuous and discrete time neural data.

Figure 1: Sample of a Sternberg recognition memory task: each trial starts with a probe (asterisk), followed by 4 stimuli (letters in this case) and a probe ("Probe"). After the response has been given ("Response"), the subject receives feedback("Feedback") presses a button to advance to the next trial ("Key").

Figure 2: Intracranial EEG data exhibits significant task-related non-stationarity, predominantly in the theta frequency band. Frequency-domain non-stationarity is calculated by expanding the spectrogram, S(f,t) along an orthogonal set of basis functions. The statistical properties of the coefficients can be used to quantify whether the statistics of the spectral components vary in time.

Figure 3: For every trial (extent of each trial is indicated by the white bar) oscillations in the theta band (4-8 Hz) is gated (i.e. it turns on at the start of the trial and turns off at the end).

Figure 4: Spectral analysis of spike trains recorded in the prefrontal cortex of a macaque monkey during an object working memory task. The spectral properties during the memory period are significantly different from the baseline period (note the "dip" in the low frequency range).