Laplace Approximations for Variances of Estimators Based on Categorical Data in Presence of Unreported Items

The method of Laplace is an analytical tool to approximate intractable posterior expectations. It trades the problems of ambiguous convergence in time associated with asymptotic computational procedures (such as MCMC's) for an analytical challenge. The advantage of the method of Laplace is that, once the analytical difficulties are resolved, then, unlike asymptotic computational procedures, the method of Laplace can be applied repeatedly, and virtually instantaneously, with a quantifiable error. The natural question: is it worth the extra analytical burden? A~(o"ff2) = l o g ( f l ( O c ) ) + l o g ( p ( c r ) )