1. Statistical analysis and modeling of neural data Lecture 5 Bijan Pesaran 19 Sept, 2007

2. Goals Recap last lecture – review Poisson process Give some point process examples to illustrate concepts. Characterize measures of association between observed sequences of events.

3. Poisson process

4. Renewal process Independent intervals Completely specified by interspike interval density Convolution to get spike counts

5. Characterization of renewal process Parametric: Model ISI density. –Choose density function, Gamma distribution: –Maximize likelihood of data No closed form. Use numerical procedure.

6. Characterization of renewal process Non-parametric: Estimate ISI density –Select density estimator –Select smoothing parameter

7. Non-stationary Poisson process – Intensity function

8. Conditional intensity function

9. Measures of association Conditional probability Auto-correlation and cross correlation Spectrum and coherency Joint peri-stimulus time histogram

10. Cross intensity function

11. Cross-correlation function

12. Limitations of correlation It is dimensional so its value depends on the units of measurement, number of events, binning. It is not bounded, so no value indicates perfect linear relationship. Statistical analysis assumes independent bins

13. Scaled correlation This has no formal statistical interpretation!

14. Corrections to simple correlation Covariations from response dynamics Covariations from response latency Covariations from response amplitude

15. Response dynamics Shuffle corrected or shift predictor

16. Joint PSTH

17. Questions Is association result of direct connection or common input Is strength of association dependent on other inputs