infonet-economy

In this thesis I investigate the validity and the accuracy properties of the posterior quantiles in Bayesian statistics when replacing the parametric likelihood with the Cressie-Read empirical likelihoods based on a set of unbiased M-estimating equations. At first order I study the validity of the empirical posterior distribution derived from the pseudo-likelihood constructed with profiled weights and estimated at a minimum distance from the empirical distribution in the Cressie-Read family of divergences, indexed by γ. The bias in coverage of the resulting empirical posterior quantile is inversely proportional to the asymptotic efficiency of the estimator corresponding to the set of M-estimating functions. By comparing different members of the Cressie-Read family of empirical likelihoods for models in the exponential family, I establish a hierarchy in the accuracy of the quantile function of the empirical posterior distribution depending on the index parameter γ.