Statistical analysis and modeling of neural data Lecture 17 Bijan Pesaran 12 November, 2007.

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]