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Statistical analysis and modeling of neural data Lecture 17

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. Spectrum. power. Spike times. 1/T. +. power. =. T. Coherency. frequency. High. Low.

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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]

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