  This article contains two main theoretical results on neural spike train
models. The first assumes that the spike train is modeled as a counting or
point process on the real line where the conditional intensity function is a
product of a free firing rate function s, which depends only on the stimulus,
and a recovery function r, which depends only on the time since the last spike.
If s and r belong to a q-smooth class of functions, it is proved that sieve
maximum likelihood estimators for s and r achieve essentially the optimal
convergence rate (except for a logarithmic factor) under L_1 loss.
  The second part of this article considers template matching of multiple spike
trains. P-values for the occurrences of a given template or pattern in a set of
spike trains are computed using a general scoring system. By identifying the
pattern with an experimental stimulus, multiple spike trains can be deciphered
to provide useful information.
