When AssociationMap::ClassifyTargets generates the likelihood values that are set in the result TargetClassification, what exactly are the data that is used to generate this score?

Said differently, I understand that the result value is the likelihood that a given stimulus is associated with an ERP, but what data are used to generate this likelihood? What is the numerical significance of the number?

Also, what is the "zero" value for this score? My experiments result in both positive and negative values, and I've questioned whether the polarity of the value is an important consideration, i.e. whether 0 is a higher likelihood than -20, or the reverse is true.

Thanks,

Doug Davies

## Classify Targets Likelihood Values

### Re: Classify Targets Likelihood Values

Hi,

thank you for your questions. Actually, the comments in the code are not quite correct when referring to "likelihood"; rather, the values in question are linear functions of log-likelihood ratios. This may have caused some confusion, sorry.

To answer your questions:

The input to AssociationMap::ClassifyTargets() is computed by the P3SignalProcessing module. For each stimulus (row or column), wave forms are projected onto the LinearClassifier classification vector (which is actually a vector but looks like a matrix because it processes wave forms organized into channels and time offsets).

Thus, the output of the P3SignalProcessing module is the output of a linear classification function. Under the assumption that noise is Gaussian distributed with equal covariances for both classes, this output is a log-likelihood ratio for the data to belong to either of the two classes (http://en.wikipedia.org/wiki/Linear_dis ... t_analysis).

So the input to AssociationMap::ClassifyTargets() is a log-likelihood ratio for the existence of an ERP vs. the non-existence of an ERP, up to a constant offset and a constant positive scaling factor.

AssociationMap::ClassifyTargets() then computes, for each target, the average of that value, taken over all instances of target presentation, i.e. over all epochs and row or column presentations. That average, again, is a linear function of the average log-likelihood ratio for each target. Therefore, choosing the target with the greatest value amounts to selecting the target for which most evidence exists that it elicited an ERP.

From this, it should be clear that 0 represents a higher likelihood ratio than -20, so the target with a value of 0 should be selected over a target with value -20.

Regards,

Juergen

thank you for your questions. Actually, the comments in the code are not quite correct when referring to "likelihood"; rather, the values in question are linear functions of log-likelihood ratios. This may have caused some confusion, sorry.

To answer your questions:

The input to AssociationMap::ClassifyTargets() is computed by the P3SignalProcessing module. For each stimulus (row or column), wave forms are projected onto the LinearClassifier classification vector (which is actually a vector but looks like a matrix because it processes wave forms organized into channels and time offsets).

Thus, the output of the P3SignalProcessing module is the output of a linear classification function. Under the assumption that noise is Gaussian distributed with equal covariances for both classes, this output is a log-likelihood ratio for the data to belong to either of the two classes (http://en.wikipedia.org/wiki/Linear_dis ... t_analysis).

So the input to AssociationMap::ClassifyTargets() is a log-likelihood ratio for the existence of an ERP vs. the non-existence of an ERP, up to a constant offset and a constant positive scaling factor.

AssociationMap::ClassifyTargets() then computes, for each target, the average of that value, taken over all instances of target presentation, i.e. over all epochs and row or column presentations. That average, again, is a linear function of the average log-likelihood ratio for each target. Therefore, choosing the target with the greatest value amounts to selecting the target for which most evidence exists that it elicited an ERP.

From this, it should be clear that 0 represents a higher likelihood ratio than -20, so the target with a value of 0 should be selected over a target with value -20.

Regards,

Juergen

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