where "s" is the dimension of formula_32 and formula_150 and formula_151 are hyperparameters (parameters controlling parameters). formula_152 corresponds to the effective number of observations that the prior distribution contributes, and formula_151 corresponds to the total amount that these pseudo-observations contribute to the sufficient statistic over all observations and pseudo-observations. formula_154 is a normalization constant that is automatically determined by the remaining functions and serves to ensure that the given function is a probability density function (i.e. it is normalized). formula_155 and equivalently formula_74 are the same functions as in the definition of the distribution over which π is the conjugate prior.