Journal of Neuroscience Methods 169 (2008) 391–404 Responses of neurons in the inferior colliculus to binaural disparities: Insights from the use of Fisher information and mutual information Noam Gordon a , Trevor M. Shackleton b , Alan R. Palmer b , Israel Nelken a,c,∗ a Department of Neurobiology, Silberman Institute of Life Sciences, Edmund Safra Campus, Hebrew University, Givat Ram, Jerusalem 91904, Israel b MRC Institute of Hearing Research, University Park, Nottingham NG7 2RD, UK c Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem 91904, Israel Received 31 July 2007; received in revised form 4 November 2007; accepted 10 November 2007 Abstract The minimal change in a stimulus property that is detectable by neurons has been often quantified using the receiver operating characteristic (ROC) curve, but recent studies introduced the use of the related Fisher information (FI). Whereas ROC analysis and FI quantify the information available for discriminating between two stimuli, global aspects of the information carried by a neuron are quantified by the mutual information (MI) between stimuli and responses. FI and MI have been shown to be related to each other when FI is large. Here the responses of neurons recorded in the inferior colliculus of anesthetized guinea pigs in response to ensembles of sounds differing in their interaural time differences (ITDs) or binaural correlation (BC) were analyzed. Although the FI is not uniformly large, there are strong relationships between MI and FI. Information-theoretic measures are used to demonstrate the importance of the non-Poisson statistics of these responses. These neurons may reflect the maximization of the MI between stimuli and responses under constraints on the coded stimulus range and the range of firing rates. Remarkably, whereas the maximization of MI, in conjunction with the non-Poisson statistics of the spike trains, is enough to create neurons whose ITD discrimination capabilities are close to the behavioral limits, the same rule does not achieve single-neuron BC discrimination that is as close to behavioral performance. © 2007 Elsevier B.V. All rights reserved. Keywords: Auditory system; Binaural disparities; Inferior colliculus; Guinea pig; Fisher information; Mutual information 1. Introduction Developing the appropriate tools for the quantification of neural responses to sensory stimuli is an important goal in neuroscience. Throughout the modern history of neuroscience, the availability of the right quantifiers of stimulus–response relationships has been crucial for scientific advances. Thus, the study of auditory sensory coding cannot be imagined today without tools such as the peristimulus time histogram introduced by Gerstein (1960), reverse correlation techniques initially introduced by De Boer (1968,1969), or the concept of the spectro-temporal receptive field (Aertsen and Johannesma, 1980, 1981; Aertsen et al., 1981). ∗ Corresponding author at: Department of Neurobiology, Silberman Insti- tute of Life Sciences, Edmund Safra Campus, Hebrew University, Givat Ram, Jerusalem 91904, Israel. Tel.: +972 2 6584229; fax: +972 2 6586077. E-mail address: Israel@cc.huji.ac.il (I. Nelken). While all of the quantifiers above are important for under- standing how a stimulus affects neuronal responses, a separate toolkit has been developed in order to study the reverse question—how can the nervous system use neuronal responses in order to extract information about the environment. Typically, such studies start with a set of relevant stimuli (e.g. broad- band noise presented from many different directions in space, Middlebrooks et al., 1994). To evaluate the discrimination based on single trials, a classifier is trained to use the response recorded in single trials in order to identify the stimulus that gave rise to the response. A large number of different classifiers have been used for the general problem of classifying neuronal responses. However, this approach is inherently ad hoc: there may always be yet another, better classifier that will achieve a higher discrimination performance based on the same responses. It turns out that the performance of all classifiers on a given set of responses can in fact be uniformly bounded. For this purpose, the performance of a classifier is quantified by the so-called transmitted information. 0165-0270/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jneumeth.2007.11.005