Point Process Spectral Analysis Examples
Example #1: Simple Poisson Process
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Poisson ISI Histogram
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ISI (msec)
Sample Spectrum from Poisson Data
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0.45 0.4
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Frequency (kHz)
Power (Hz)
Example #1: Simple Poisson Process
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Example #2: Hard Refractory Period
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Poisson ISI Histogram
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ISI (msec)
Refractory Process ISI Histogram
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ISI (msec)
Sample Spectrum from Poisson Data
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Frequency (kHz)
Power (Hz)
Refractory Process Sample Spectrum
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Power (Hz)
Example #1: Simple Poisson Process
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Example #3: Duplicate each spike at 10 ms lag
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10 ms Repetition ISI Histogram
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ISI (msec)
Repeated Spike Sample Spectrum
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Example #4: Realistic Baseline Spiking Data
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Baseline Spiking ISI
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ISI (msec)
Sample Spectrum for Baseline Spiking
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Case 1: An Analysis of the Spiking Activity of Retinal Neurons in Culture (Iygengar and Liu, 1997)
Retinal neurons are grown in culture under constant light and environmental conditions. The spontaneous spiking activity of these neurons is recorded. The objective is to develop a statistical model which accurately describes the stochastic structure of this activity.
Retinal Baseline Data Spectrum
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Power (Hz)
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Frequency (Hz)
Retinal Baseline Data Spectrogram
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Time (sec)
Frequency (Hz)
Autocorrelation of interspike intervals
1.2 1 0.8 0.6 0.4 0.2 0 -0.2
-10 -8 -6 -4 -2 0 2 4 6 8 10
Lag
Correlation coefficient
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0.4 0.45 0.5
Interval Spectrum
Inverse Lag
Power
0.12
0.1
0.08
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ISI Histogram
Exponential Gamma
Inverse Gaussian Order 50 GLM
ISI (msec)
Probability Density
Hippocampal Place Field
1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
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Hippocampal Place Field
Place Field Spectrogram
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Frequency (Hz)
Place Field Spectrogram
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Time (msec)
Frequency (Hz)
Place Field Analysis from Problem Set #3
S ⎧∑p ⎫ λ(t | H ) = λ (xN(t),yN(t))exp β ⋅spikes_hist(:,i)
t
⎨⎬
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i
⎩i=1 ⎭
0 0.2 0.4 0.6 0.8 1
Empirical CDF
Model CDF
Conclusions
• Point process spectral analysis is useful for visualizing point process data and suggesting classes of conditional intensity models.
• The interpretation of sample point process spectra differs from that of continuous valued signals.