1. Statistical analysis and modeling of neural data Lecture 7 Bijan Pesaran 26 Sept, 2007

2. Goals Recap – spectral analysis for point processes. Coherency/Partial coherency as linear measures of association. Time-rescaling theorem and model validation

3. Spectral analysis for point processes Regression for temporal sequences Naturally leads to measures of correlation Statistical properties of estimators well- behaved

4. Cross-spectral density

5. Spectral quantities

6. Coherence as linear association

7. Minimum value is: Where: Minimize wrt B(f): Substitute into loss:

8. Time lags in coherency

9. Partial coherence

11. Time-rescaling theorem Poisson with rate 1 History-dependent time rescaling

12. Kolmogorov-Smirnov Test Empirical distribution function Critical values of the Kolmogorov-Smirnov Distribution

13. Kolmogorov-Smirnov Test Test for deviation from uniform distribution Construct cumulative distribution function Rank vs (95% confidence)(99% confidence)