Simultaneous confidence bands for (Markov chain) Monte Carlo simulations

Oregon Convention Center 

We consider the construction of simultaneous confidence bands (CBs) for functional parameters over uncountable sets in Monte Carlo simulations. This setting arises naturally in estimating one or more marginal posterior densities, which may be done nonparametrically or via Rao-Blackwellisation. Although our motivation is primarily in estimating and visualizing densities, our approach can be applied in more general functional estimation, such as in estimation of likelihood functions for likelihood-based inference and when functional parameters are of interest in Bayesian inference. In short, we provide principled uncertainty quantification in the form of a simultaneous CB and hence increase the reliability of the resulting functional inference.