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Dynamically rescaled Hamiltonian Monte Carlo (DRHMC) is introduced as acomputationally fast and easily implemented method for performing full Bayesiananalysis in hierarchical statistical models. The method relies on introducing amodified parameterisation so that the re-parameterised target distribution hasclose to constant scaling properties, and thus is easily sampled using standard(Euclidian metric) Hamiltonian Monte Carlo. Provided that the parameterisationsof the conditional distributions specifying the hierarchical model are"constant information parameterisations" (CIP), the relation between themodified- and original parameterisation is bijective, explicitly computed andadmit exploitation of sparsity in the numerical linear algebra involved. CIPsfor a large catalogue of statistical models are presented, and from thecatalogue, it is clear that many CIPs are currently routinely used instatistical computing. A relation between the proposed methodology and a classof explicitly integrated Riemann manifold Hamiltonian Monte Carlo methods isdiscussed. The methodology is illustrated on several example models, includinga model for inflation rates with multiple levels of non-linearly dependentlatent variables.

Dynamically rescaled Hamiltonian Monte Carlo for Bayesian Hierarchical Models