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

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Presentation transcript:

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