Statistical analysis and modeling of neural data

Lecture 17

Bijan Pesaran

12 November, 2007

Goals• Practical issues of spectral representation

• Spectral estimation problem

• Examples on real data

Spectral intuition

=tv

LFP Voltage +

Spectrum

pow

er

1/T

ntSpike times

=T

frequency

pow

er

Low High 0

Spikes

Field

Coherency

Fundamental concepts

• Positive and negative frequency

• Nyquist frequency – aliasing

• Rayleigh frequency

• Spectral density and power

ttk coscos

t cos

K even

K odd

dffS2/1

0

2 )(2

The spectral estimation problem

Consistency and bias

Example I: LFP spectrograms

• Estimation issues– Bias

• Narrow band• Broad band

– Variance

– Degrees of freedom

Example I: LFP spectrograms

• Confidence intervals– Chi2

• Assume Gaussian process

– Jackknife• Does not assume Gaussian process

Example I: LFP spectrograms

• Example recordingCue CueSaccade Saccade

Example I: LFP spectrograms

Periodogram – Single Trial Multitaper estimate- Single Trial, [5,9]

Periodogram – Single Trial

Multitaper estimate- Single Trial

Example I: LFP spectrograms

Example I: LFP spectrograms

Multitaper estimate- Single Trial [5,9]

Multitaper estimate- Nine Trials [5,9]

Example I: LFP spectrograms

Multitaper estimate- Single Trial

Multitaper estimate- Nine Trials

Example I: LFP spectrograms

Multitaper estimate- 95% Chi2

212~ dofS

Multitaper estimate- 95% Jackknife

Leave-one-out

Example I: LFP spectrograms

Time (s)

Fre

quen

cy (

Hz)

-0.5 0 0.5 1 1.50

50

100

5

10

15

20

25

Multitaper estimate- T = 0.5s, W = 10Hz

Time (s)

Fre

quen

cy (

Hz)

-0.5 0 0.5 1 1.50

50

100

150

5

10

15

20

25

Multitaper estimate- T = 0.2s, W = 25Hz

Example II: Spike rates, spectra and coherence

Auto-correlation fn Multitaper spectrum[8,15]

Example II: Spike rates, spectra and coherence

Cross-correlation fn Multitaper coherence9 trials, [8,15]

Example II: Spike rates, spectra and coherence

Multitaper coherence9 trials, [12,23]

Multitaper coherence9 trials, [8,15]