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Statistical analysis and modeling of neural data Lecture 17

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##### Statistical analysis and modeling of neural data Lecture 17

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**Statistical analysis and modeling of neural dataLecture 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 Spikes Field Spectral intuition = LFP Voltage**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**Cue**Saccade Cue Saccade Example I: LFP spectrograms • Example recording**Multitaper estimate**- Single Trial, [5,9] Periodogram – Single Trial Example I: LFP spectrograms**Example I: LFP spectrograms**Periodogram – Single Trial Multitaper estimate - Single Trial**Multitaper estimate**- Nine Trials [5,9] Example I: LFP spectrograms Multitaper estimate - Single Trial [5,9]**Example I: LFP spectrograms**Multitaper estimate - Single Trial Multitaper estimate - Nine Trials**Multitaper estimate**- 95% Jackknife Leave-one-out Example I: LFP spectrograms Multitaper estimate - 95% Chi2**Multitaper estimate**- T = 0.2s, W = 25Hz Example I: LFP spectrograms Multitaper estimate - T = 0.5s, W = 10Hz**Example II: Spike rates, spectra and coherence**Multitaper spectrum [8,15] Auto-correlation fn**Example II: Spike rates, spectra and coherence**Multitaper coherence 9 trials, [8,15] Cross-correlation fn**Example II: Spike rates, spectra and coherence**Multitaper coherence 9 trials, [8,15] Multitaper coherence 9 trials, [12,23]