Statistical analysis and modeling of neural data Lecture

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

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

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

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

Non-stationary Poisson process – Intensity function

Conditional intensity function

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

Cross intensity function

Cross-correlation function

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

Scaled correlation • This has no formal statistical interpretation!

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

Response dynamics • Shuffle corrected or shift predictor

Joint PSTH

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