Coding with noisy neurons: stability of tuning curve estimation strongly depends on the analysis method

An important issue in the neurosciences is a quantitative description of the relation between sensory stimuli presented to an animal and their representations in the nervous system. A standard technique is the construction of a neural tuning curve, that is, a neuron's average firing rate as a function of some parameter characterizing a family of stimuli. It is unavoidable that some of the response data are erroneously attributed to a cell, e.g., during spike sorting. However, the widely used method of statistical analysis based on the sample mean and least-squares approximation for the spike count can perform extremely badly if the noise distribution is not exactly normal, which is almost never the case in applications. Here, we present a method for constructing neural tuning curves that is especially suited for cases of high noise and the presence of outliers. Since it is usually not decidable if an outlier is faulty or not we limit the influence of far outlying points rather than try to identify and discard them. In contrast to traditional methods employing a point-by-point estimation of a tuning curve, we use all measured data from all different stimulus conditions at once in the construction. Given the measured data at only a finite number of stimulus conditions, a robust tuning curve is obtained that approximates the cell's ideal tuning curve optimally in all stimulus conditions with respect to a given distance measure. A measure that assesses the quality of this fitting method with respect to the traditional least-squares fitting method and to a median-based fitting method is introduced. The reliability of inference with respect to the encoding accuracy that can be achieved by a population of neurons is demonstrated in both artificially generated and experimentally recorded data from rat primary visual cortex. While the data shown in this paper are responses to orientation stimuli, the method of tuning curve construction is also viable and maintains its optimality properties for the case in which the stimulus is defined on a finite interval.