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

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

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

  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

  8. Cue Saccade Cue Saccade Example I: LFP spectrograms • Example recording

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

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

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

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

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

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

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

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

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