2018/06/06 by Tore Selland Kleppe, Kleppe, Tore Selland · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1806.02068
openalex publication_date 2018/06/06 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Dynamically rescaled Hamiltonian Monte Carlo (DRHMC) is introduced as a computationally fast and easily implemented method for performing full Bayesian analysis in hierarchical statistical models. The method relies on introducing a modified parameterisation so that the re-parameterised target distribution has close to constant scaling properties, and thus is easily sampled using standard (Euclidian metric) Hamiltonian Monte Carlo. Provided that the parameterisations of the conditional distributions specifying the hierarchical model are "constant information parameterisations" (CIP), the relation between the modified- and original parameterisation is bijective, explicitly computed and admit exploitation of sparsity in the numerical linear algebra involved. CIPs for a large catalogue of statistical models are presented, and from the catalogue, it is clear that many CIPs are currently routinely used in statistical computing. A relation between the proposed methodology and a class of explicitly integrated Riemann manifold Hamiltonian Monte Carlo methods is discussed. The methodology is illustrated on several example models, including a model for inflation rates with multiple levels of non-linearly dependent latent variables.