4_quantitative

4_quantitative - Harvard-MIT Division of Health Sciences...

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Harvard-MIT Division of Health Sciences and Technology HST.722J: Brain Mechanisms for Hearing and Speech Course Instructor: Bertrand Delgutte Quantitative approaches to the study of neural coding ©Bertrand Delgutte, 2003-2005
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The Problem Neural and behavioral data have different forms that are not easily comparable – In some cases, data from different species and states (awake vs. anesthetized) are being compared – Even when neural and behavioral data have similar forms (e.g. a threshold), they both depend on arbitrary criteria Both neural and behavioral responses are probabilistic: They are not identical for different repetitions of the same stimulus. Therefore, they provide a noisy (imprecise) representation of the stimulus. Are there quantitative tools to describe the precision of stimulus representation in neural and behavioral data?
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Questions that can be addressed by quantitative methods Does a particular class of neurons provide sufficient information to account for performance in a particular behavioral task? Does a particular neural code (e.g. rate-place vs. temporal) provide sufficient information for the task? Which stimulus feature is a particular neuron or neural population most sensitive to? Are there “feature detector” neurons? Is there stimulus information in the correlated firings of groups of neurons? How efficient is the neural code?
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Outline • Signal detection theory (a.k.a. ideal observer analysis) – Single neuron – Combined performance for neural population • Shannon information theory
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Neural variability limits detection performance When a sound stimulus is presented repeatedly, the number of spikes recorded from an auditory neuron differs on each trial. The blue and red surfaces are model spike count distributions for two pure tones differing in intensity by 3 dB. The overlap in the spike count distributions limits our accuracy in identifying which of the two stimuli was presented based on the responses of this neuron. A measure of the separation between the two distributions (and therefore of the neuron’s ability to discriminate) is the discriminability index d’ , which is the difference in means of the two distributions divided by their standard deviation. The just noticeable difference (JND) or difference limen (DL) is often taken as the intensity increment for which d’ = 1. This criterion corresponds to 76% correct in a two-interval, two-alternative psychophysical experiment. Delgutte (unpublished)
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Conditional Probability and Bayes’ Rule Conditional Probability: Statistically Independent Events: Bayes’ Rule: ( | )( , ) / ( ) PS R PSR PR = (, ) () () (|) () PSR PS PR PS = = (|)() P RSPS PR =
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Bayesian Optimal Decision and the Likelihood Ratio The Problem: Choose between two alternatives (stimuli) S0 and S1 with prior probabilities P(S0) and P(S1) given the observation (neural response) R so as to minimize the probability of error.
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4_quantitative - Harvard-MIT Division of Health Sciences...

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