The likelihood is just the binomial, with parameters 
. Let 
be the data, 
be the data up to time
point N, and 
be the parameters, with 
being the hyperparameters. Let 
represent the collection
of all 
.
Then, the likelihood is given as
since 
independent of 
conditional on . And, this is just
Certainly one is interested in predicting 
given 
and the
.