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Statistical analysis and modeling of neural data Lecture 6

Statistical analysis and modeling of neural data Lecture 6. Bijan Pesaran 24 Sept, 2007. Goals. Recap last lecture – review time domain point process measures of association Spectral analysis for point processes Examples for illustration. Questions.

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Statistical analysis and modeling of neural data Lecture 6

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  1. Statistical analysis and modeling of neural dataLecture 6 Bijan Pesaran 24 Sept, 2007

  2. Goals • Recap last lecture – review time domain point process measures of association • Spectral analysis for point processes • Examples for illustration

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

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

  5. Cross-correlation function

  6. Cross-correlation function

  7. 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

  8. Scaled correlation • This has no formal statistical interpretation!

  9. Corrections to simple correlation • Covariations from response dynamics • Covariations from response latency • Covariations from response amplitude

  10. Response dynamics • Shuffle corrected or shift predictor

  11. Non-stationarity • Assume moments of the distribution constant over time. • Simplest solution is to assume stationarity is local in time • Moving window analysis

  12. Joint PSTH

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

  14. Cross-spectral density

  15. Spectral representation for point processes

  16. Spectral quantities

  17. Spectral examples • Refractoriness – Underdispersion • Fourier transform of Gaussian variable • Bursting – Overdispersion • Cosine function

  18. Coherence as linear association

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

  20. Time lags in coherency

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