1 / 17

Statistical analysis and modeling of neural data Lecture 5

This lecture by Bijan Pesaran on Sept 19, 2007, covers Poisson and Renewal processes, measures of association in neural data, characterization techniques, and limitations and corrections in correlation analysis.

stevef
Download Presentation

Statistical analysis and modeling of neural data Lecture 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related