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

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

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

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

5. The spectral estimation problem Consistency and bias

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

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

10. Example I: LFP spectrograms Example recording Cue Saccade

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

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

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

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

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

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

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

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

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