Advances in approximate Bayesian computation with modified pseudo-likelihood roots
Erlis Ruli, Laura Ventura · 2013
The likelihood function plays a central role in the theory of higher-order asymptotics both for Bayesian and frequentist inference. This theory provides accurate approximations to posterior distributions and to related quantities, even for small sample sizes. Moreover, these approximations give rise to a simple simulation scheme, alternative to MCMC, for Bayesian computation of marginal posterior distributions for a scalar parameter.\\\\ However, in complex models or in the presence of minimal assumptions on the model, the likelihood function may be unfeasible and pseudo-likelihood functions (such as the composite, the empirical, the quasi- and the partial likelihood) may be used as a basis for Bayesian inference. This paper aims to discuss higher-order asymptotics for Bayesian computation of pseudo-posterior distributions, e.g. posterior distributions based on suitable pseudo-likelihood functions, and to the corresponding tail area probabilities, for practical use in Bayesian analysis. The method is illustrated by two examples.