Statistical analysis and modeling of neural data Lecture 5

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Statistical analysis and modeling of neural
dataLecture 5

• Bijan Pesaran
• 19 Sept, 2007

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Goals

• Recap last lecture review Poisson process
• Give some point process examples to illustrate
  concepts.
• Characterize measures of association between
  observed sequences of events.

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Poisson process
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Renewal process

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

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Characterization of renewal process

• Parametric Model ISI density.
• Choose density function, Gamma distribution
• Maximize likelihood of data

No closed form. Use numerical procedure.
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Characterization of renewal process

• Non-parametric Estimate ISI density
• Select density estimator
• Select smoothing parameter

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Non-stationary Poisson process Intensity
function
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Conditional intensity function
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Measures of association

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

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Cross intensity function
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Cross-correlation function
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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

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Scaled correlation

• This has no formal statistical interpretation!

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Corrections to simple correlation

• Covariations from response dynamics
• Covariations from response latency
• Covariations from response amplitude

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Response dynamics

• Shuffle corrected or shift predictor

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Joint PSTH
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Questions

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