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.