  A cornerstone of human statistical learning is the ability to extract
temporal regularities / patterns from random sequences. Here we present a
method of computing pattern time statistics with generating functions for
first-order Markov trials and independent Bernoulli trials. We show that the
pattern time statistics cover a wide range of measurements commonly used in
existing studies of both human and machine learning of stochastic processes,
including probability of alternation, temporal correlation between pattern
events, and related variance / risk measures. Moreover, we show that recurrent
processing and event segmentation by pattern overlap may provide a coherent
explanation for the sensitivity of the human brain to the rich statistics and
the latent structures in the learning environment.
