A general framework for parametrisation of hierarchical models
O. Papaspiliopoulos, G. O. Roberts and M. Sköld
Centre for Mathematical Sciences
Lund Institute of Technology,
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.