  We present a technique for constructing suitable posterior probability
distributions in situations for which the sampling distribution of the data is
not known. This is very useful for modern scientific data analysis in the era
of "big data", for which exact likelihoods are commonly either unknown,
computationally prohibitively expensive or inapplicable because of systematic
effects in the data. The scheme involves implicitly computing the changes in an
approximate sampling distribution as model parameters are changed via
explicitly-computed moments of statistics constructed from the data.
