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SUMMARY:Riemannian Manifold Hamiltonian Monte Carlo - Mark Girolami
DTSTART:20100121T140000Z
DTEND:20100121T150000Z
UID:TALK22644@talks.cam.ac.uk
CONTACT:Microsoft Research Cambridge Talks Admins
DESCRIPTION:*Abstract:* The talk will present a Riemannian Manifold Hamilt
 onian Monte Carlo sampler that resolves the shortcomings of existing Monte
  Carlo algorithms when sampling from target densities that may be high dim
 ensional and exhibit strong correlations. The correctness of the method is
  proven and it is demonstrated that it provides a fully automated adaptati
 on mechanism that circumvents the costly pilot runs required to tune propo
 sal densities for Metropolis-Hastings or indeed Hybrid Monte Carlo and Met
 ropolis Adjusted Langevin Algorithms. This allows for highly efficient sam
 pling even in very high dimensions where different scalings may be require
 d for the transient and stationary phases of the Markov chain. The propose
 d method exploits the Riemannian structure of the parameter space of stati
 stical models and thus automatically adapts to the local manifold structur
 e at each step based on the metric tensor. A semi-explicit second order sy
 mplectic integrator for non-separable Hamiltonians is derived for simulati
 ng paths across this manifold which provides highly efficient convergence 
 and exploration of the target density. The performance of the Riemannian M
 anifold Hamiltonian Monte Carlo method is assessed by performing posterior
  inference on logistic regression models\, log-Gaussian Cox point processe
 s\, stochastic latent volatility models\, and Bayesian estimation of param
 eter posteriors of dynamical systems described by nonlinear differential e
 quations. Substantial improvements in the time normalised Effective Sample
  Size are reported when compared to alternative sampling approaches. Matla
 b codes are available at http://www.dcs.gla.ac.uk/inference/rmhmc
LOCATION:Small public lecture room\, Microsoft Research Ltd\, 7 J J Thomso
 n Avenue (Off Madingley Road)\, Cambridge
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