Information content in threshold data with non-Gaussian noise

摘要

If data is binary, it is probable that the combination of a signal of interest plus a noise has been simplified by a thresholding mechanism, as in, e.g., a neuron firing mechanism. For identifying optimal signal or coding range of binary data, Fisher information is an attractive measure. A general formula allows the signal level or signal range producing the most information-rich data to be identified if the noise distribution is known. In this paper we study the information content of binary data resulting from threshold exceedance of a signal plus an arbitrary type of noise. For a specified parametric family of distributions a fixed proportion of exceedances is optimal for any combination of signal, threshold, and noise amplitude. If the ratio of noise to signal level is constant, Fisher information is unimodal for many noise distributions. The results extend to the case of a random signal and to inter-exceedance-interval data. The family of gamma noise distributions is used for illustration.