The expression given in Eq. (5) for the mutual information is in practice difficult to evaluate because estimating the distributions , and may require very large amounts of data. For example, suppose that there are 1000 input spike trains driving the output, and that each spike train is divided into segments 100 msec in length, and discretized into 1 msec bins. There are then possible output spike trains, sets of input spike trains, and possible combinations of input and output spike trains forming the space over which the joint distribution must be estimated. While this naive calculation is in practice an overestimate (see [de Ruyter van Steveninck et al., 1997, Buracas et al., 1996] for methods that make use of the fact that most spike trains are very unlikely), it emphasizes the potential problems involved in estimating the mutual information. Below we describe two practical methods for computing information rates.