Likelihood approaches to sensory coding in auditory cortex

Likelihood methods began their evolution in the early 1920s with R A Fisher, and have developed into a rich framework for inferential statistics. This framework offers tools for the analysis of the differential geometry of the full likelihood function based on observed data. We examine likelihood functions derived from inverse Gaussian (IG) probability density models of cortical ensemble responses of single units. Specifically, we investigate the problem of sound localization from the observation of an ensemble of neural responses recorded from the primary (AI) field of the auditory cortex. The problem is framed as a probabilistic inverse problem with multiple sources of ambiguity. Observed and expected Fisher information are defined for the IG cortical ensemble likelihood functions. Receptive field functions of multiple acoustic parameters are constructed and linked to the IG density. The impact of estimating multiple acoustic parameters related to the direction of a sound is discussed, and the implications of eliminating nuisance parameters are considered. We examine the degree of acuity afforded by a small ensemble of cortical neurons for locating sounds in space, and show the predicted patterns of estimation errors, which tend to follow psychophysical performance.