A signal-to-noise ratio estimator for generalized linear model systems

The signal-to-noise ratio (SNR) is a commonly used measure of system fidelity estimated as the ratio of the variance of a signal to the variance of the noise. Although widely used in analyses of physical systems, this estimator is not appropriate for point process models of neural systems or other non-Gaussian and/or non-additive signal and noise systems. We show that the extension of the standard estimator to the class of generalized linear models (GLM) yields a new SNR estimator that is ratio of two estimated prediction errors. Each prediction error estimate is an approximate chi-squared random variable whose expected value is given by its number of degrees of freedom. This allows us to compute a new bias-corrected SNR estimator. We illustrate its application in a study of simulated neural spike trains from a point process model in which the signal is task-specific modulation across multiple trials of a neurophysiological experiment. The new estimator characterizes the SNR of a neural system in terms commonly used for physical systems. It can be further extended to analyze any system in which modulation of the system's response by distinct signal components can be expressed as separate components of a likelihood function