GLASS: A General Likelihood Approximate Solution Scheme

Abstract

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.