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Statistical analysis and modeling of neural data Lecture 5

Statistical analysis and modeling of neural data Lecture 5. Bijan Pesaran 19 Sept, 2007. Goals. Recap last lecture – review Poisson process Give some point process examples to illustrate concepts. Characterize measures of association between observed sequences of events. Poisson process.

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Statistical analysis and modeling of neural data Lecture 5

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  1. Statistical analysis and modeling of neural dataLecture 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

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