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Discussion on the paper: Riemann manifold Langevin and Hamiltonian Monte Carlo methods, by Girolami and
 

Summary: Discussion on the paper: Riemann manifold Langevin
and Hamiltonian Monte Carlo methods, by Girolami and
Calderhead
Iain Murray
School of Informatics, University of Edinburgh, UK
Ryan Prescott Adams
Department of Computer Science, University of Toronto, Canada
This is an exciting piece of work. We agree with the authors that Hamiltonian Monte
Carlo (HMC) could be used more broadly. HMC has a reputation as being difficult to tune
and we hope that the more robust behaviour demonstrated here will help alleviate this.
Dynamical methods jointly update variables, which may allow larger moves in complex
models than updating variables independently. Hierarchical models often contain strong
prior dependencies between hyperparameters and parameters and would seem to provide
a common case where HMC offers benefits. Unfortunately, updating hyperparameters and
parameters jointly using standard HMC does not necessarily work better than updating
them individually (Choo, 2000).
Consider a simple hierarchical model (Neal, 2003) where the observations are uninfor-
mative about the parameters:
v N(0, 2
), e.g., =3,

  

Source: Adams, Ryan Prescott - Department of Electrical and Computer Engineering, University of Toronto
Edinburgh, University of - Division of Informatics, Institute for Adaptive and Neural Computation
Roweis, Sam - Department of Computer Science, University of Toronto

 

Collections: Biology and Medicine; Computer Technologies and Information Sciences