A general framework for parametrisation of hierarchical models

O. Papaspiliopoulos, G. O. Roberts and M. Sköld

Abstract:: In this paper, we describe centering and non-centering methodology as complementary tecniques for use in parameterisation of broad classes of hierarchical models, with a view to the construction of effective MCMC algorithms for exploring posterior distributions from these models. We give a clear qualitative understanding as to when centering and non-centering work well, and introduce theory concerning the convergence time complexity of Gibbs samplers using centred and non-centred parameterisations. We give general recipes for the construction of non-centred parameterisations, including an auxiliary variable technique called the state-space expansion technique. We also describe partially non-centred methods, and demonstrate their use in constructing robust Gibbs sampler algorithms whose convergence properties are not overly sensitive to the data.