The estimation of the information carried by spike times is crucial for a quantitative understanding of brain function, but it is difficult because of an upward bias due to limited experimental sampling. We present new progress, based on two basic insights, on reducing the bias problem. First, we show that by means of a careful application of data-shuffling techniques, it is possible to cancel almost entirely the bias of the noise entropy, the most biased part of information. This procedure provides a new information estimator that is much less biased than the standard direct one and has similar variance. Second, we use a nonparametric test to determine whether all the information encoded by the spike train can be decoded assuming a low-dimensional response model. If this is the case, the complexity of response space can be fully captured by a small number of easily sampled parameters. Combining these two different procedures, we obtain a new class of precise estimators of information quantities, which can provide data-robust upper and lower bounds to the mutual information. These bounds are tight even when the number of trials per stimulus available is one order of magnitude smaller than the number of possible responses. The effectiveness and the usefulness of the methods are tested through applications to simulated data and recordings from somatosensory cortex. This application shows that even in the presence of strong correlations, our methods constrain precisely the amount of information encoded by real spike trains recorded in vivo.

We develop new data-robust lower-bound methods to quantify the information carried by the timing of spikes emitted by neuronal populations. These methods have better sampling properties and are tighter than previous bounds based on neglecting correlation in the noise entropy. Our new lower bounds are precise also in the presence of strongly correlated firing. They are not precise only if correlations are strongly stimulus modulated over a long time range. Under conditions typical of many neurophysiological experiments, these techniques permit precise information estimates to be made even with data samples that are three orders of magnitude smaller than the size of the response space.