Statistical analysis and modeling of neural data Lecture 17 Bijan Pesaran 12 November, 2007

Goals Practical issues of spectral representation Spectral estimation problem Examples on real data

Spectral intuition = LFP Voltage + Spectrum power 1/T Spike times = T frequency power Low High Spikes Field Coherency

Fundamental concepts Positive and negative frequency Nyquist frequency – aliasing Rayleigh frequency Spectral density and power K even K odd

The spectral estimation problem Consistency and bias

Example I: LFP spectrograms Estimation issues –Bias Narrow band Broad band –Variance –Degrees of freedom

Example I: LFP spectrograms Confidence intervals –Chi2 Assume Gaussian process –Jackknife Does not assume Gaussian process

Example I: LFP spectrograms Example recording Cue Saccade

Example I: LFP spectrograms Periodogram – Single Trial Multitaper estimate - Single Trial, [5,9]

Periodogram – Single Trial Multitaper estimate - Single Trial Example I: LFP spectrograms

Multitaper estimate - Single Trial [5,9] Multitaper estimate - Nine Trials [5,9]

Example I: LFP spectrograms Multitaper estimate - Single Trial Multitaper estimate - Nine Trials

Example I: LFP spectrograms Multitaper estimate - 95% Chi2 Multitaper estimate - 95% Jackknife Leave-one-out

Example I: LFP spectrograms Multitaper estimate - T = 0.5s, W = 10Hz Multitaper estimate - T = 0.2s, W = 25Hz

Example II: Spike rates, spectra and coherence Auto-correlation fn Multitaper spectrum [8,15]

Example II: Spike rates, spectra and coherence Cross-correlation fn Multitaper coherence 9 trials, [8,15]

Example II: Spike rates, spectra and coherence Multitaper coherence 9 trials, [12,23] Multitaper coherence 9 trials, [8,15]