JOINT GLASGOW-STRATHCLYDE SEMINARS
Arnoldo Frigessi from the Norwegian Computing Center, Oslo,
is visiting Glasgow University from Nov 17 to Nov 19.
He will give two seminars on November 17th and 18th:
Wednesday Nov 17, 1-2
In Room 1f, Mathematics Building, Glasgow University:
PENALIZED PSEUDOLIKELIHOOD INFERENCE IN SPATIAL INTERACTION MODELS
WITH COVARIATES
Abstract: Given spatially located observed random variables
$(\underline x, \underline z)=3D \{(x_i, z_i)\}_{i}$, we propose a new
method for nonparametric estimation of the potential functions of a
Markov Random Field $p(\underline x | \underline z)$, based on a
roughness penalty approach. The new estimator maximises the penalized
log-pseudolikelihood function and is a natural cubic spline. The
calculations involved do not rely on Monte Carlo simulation. We
suggest the use of B-splines to stabilise the numerical procedure.
An application in Bayesian image reconstruction is described.
Thursday Nov 18, 3.30-4.30
In Room L7.20, Livingstone Tower, University of Strathclyde
(tea from 3-3.30):
ANTITHETIC COUPLING OF TWO GIBBS SAMPLER CHAINS
Abstract: Two coupled Gibbs sampler chains, both with invariant
probability density , are run in parallel in such a way that the
chains are negatively correlated. This allows us to define an
asymptotically unbiased estimator of the expectation E(f(X)) with
respect to which achieves significant variance reduction with respect
to the usual Gibbs sampler at comparable computational cost. We show
that the variance of the estimator based on the new algorithm is
always smaller than the variance of a single Gibbs sampler chain, if
is attractive and f is monotone non-decreasing in all components of
X. For non-attractive targets , our results are not complete: The new
antithetic algorithm outperforms the standard Gibbs sampler by one
order of magnitude when is a multivariate normal density or the Ising
model. More generally, non-rigorous arguments and numerical
experiments support the usefulness of the antithetically coupled Gibbs
samplers also for other non-attractive models. In our experiments the
variance is reduced to at most a third and the efficiency also
improves significantly.
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