Show Reference: "Why aren't all deep superior colliculus neurons multisensory? A Bayes' ratio analysis"

Why aren't all deep superior colliculus neurons multisensory? A Bayes' ratio analysis. Cognitive, Affective & Behavioral Neuroscience, Vol. 4, No. 3. (September 2004), pp. 344-353 by Hans Colonius, Adele Diederich
@article{colonius-and-diederich-2004,
    abstract = {Multisensory neurons in the deep superior colliculus ({SC}) show response enhancement to cross-modal stimuli that coincide in time and space. However, multisensory {SC} neurons respond to unimodal input as well. It is thus legitimate to ask why not all deep {SC} neurons are multisensory or, at least, develop multisensory behavior during an organism's maturation. The novel answer given here derives from a signal detection theory perspective. A Bayes' ratio model of multisensory enhancement is suggested. It holds that deep {SC} neurons operate under the Bayes' ratio rule, which guarantees optimal performance-that is, it maximizes the probability of target detection while minimizing the false alarm rate. It is shown that optimal performance of multisensory neurons vis-\`{a}-vis cross-modal stimuli implies, at the same time, that modality-specific neurons will outperform multisensory neurons in processing unimodal targets. Thus, only the existence of both multisensory and modality-specific neurons allows optimal performance when targets of one or several modalities may occur.},
    author = {Colonius, Hans and Diederich, Adele},
    issn = {1530-7026},
    journal = {Cognitive, Affective \& Behavioral Neuroscience},
    keywords = {bayes, computational, cue-combination, decision-making, math, model, probability, sc},
    month = sep,
    number = {3},
    pages = {344--353},
    pmid = {15535170},
    posted-at = {2012-09-19 07:38:56},
    priority = {2},
    title = {Why aren't all deep superior colliculus neurons multisensory? {A} {B}ayes' ratio analysis.},
    url = {http://view.ncbi.nlm.nih.gov/pubmed/15535170},
    volume = {4},
    year = {2004}
}

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Colonius and Diederich argue that deep-SC neurons spiking behavior can be interpreted as a vote for a target rather than a non-target being in their receptive field.

This is similar to Anastasio et al.'s previous approach.

There are a number of problems with Colonius' and Diederich's idea that deep-SC neurons' binary spiking behavior can be interpreted as a vote for a target rather than a non-target being in their RF. First, these neurons' RFs can be very broad, and the strength of their response is a function of how far away the stimulus is from the center of their RFs. Second, the response strength is also a function of stimulus strength. It needs some arguing, but to me it seems more likely that the response encodes the probability of a stimulus being in the center of the RF.

Colonius and Diederich argue that, given their Bayesian, normative model of neurons' response behavior, neurons responding to only one sensory modality outperform neurons responding to multiple sensory modalities.

Colonius' and Diederich's explanation for uni-sensory neurons in the deep SC has a few weaknesses: First, they model the input spiking activity for both the target and the non-target case as Poisson distributed. This is a problem, because the input spiking activity is really a function of the target distance from the center of the RF. Second, they explicitly model the probability of the visibility of a target to be independent of the probability of its audibility.