Correcting for the Sampling Bias Problem in Spike Train Information Measures

University of Manchester, Faculty of Life Sciences, Manchester, United Kingdom Submitted 18 May 2007; accepted in final form 21 July 2007 ABSTRACT Information Theory enables the quantification of how much information a neuronal response carries about external stimuli and is hence a natural analytic framework for studying neural coding. The main difficulty in its practical application to spike train analysis is that estimates of neuronal information from experimental data are prone to a systematic error (called "bias"). This bias is an inevitable consequence of the limited number of stimulus-response samples that it is possible to record in a real experiment. In this paper, we first explain the origin and the implications of the bias problem in spike train analysis. We then review and evaluate some recent general-purpose methods to correct for sampling bias: the Panzeri-Treves, Quadratic Extrapolation, Best Universal Bound, Nemenman-Shafee-Bialek procedures, and a recently proposed shuffling bias reduction procedure. Finally, we make practical recommendations for the accurate computation of information from spike trains. Our main recommendation is to estimate information using the shuffling bias reduction procedure in combination with one of the other four general purpose bias reduction procedures mentioned in the preceding text. This provides information estimates with acceptable variance and which are unbiased even when the number of trials per stimulus is as small as the number of possible discrete neuronal responses. Address for reprint requests and other correspondence: S. Panzeri, University of Manchester, Faculty of Life Sciences, The Mill, PO Box 88, Manchester M60 1QD,UK (E-mail: s.panzeri{at}manchester.ac.uk )