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

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

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

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

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The spectral estimation problem Consistency and bias

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

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

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Example I: LFP spectrograms Example recording Cue Saccade

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

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

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

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

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

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

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

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

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

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