The expectation of the conditional properties of Zi|Yi yields marginal properties of the
sample counts, Zi. The sample binomial counts have expectation E(Zi) = ni⇡ and variance
V ar(Zi) = ni%2
Y (ni ! 1) + ni⇡(1 ! ⇡), where ⇡ and %2
Y are the mean and variance of the
latent beta field respectively
i .