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Statistical analysis and modeling of neural data Lecture 6

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Title: A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects Author – PowerPoint PPT presentation

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Title: Statistical analysis and modeling of neural data Lecture 6


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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