The pairwise influence matrix of Dobrushin has long been used as an analytical tool to bound the rate of convergence of Gibbs sampling. In this work, we use Dobrushin influence as the basis of a practical tool to certify and efficiently improve the quality of a Gibbs sampler. Our Dobrushin-optimized Gibbs samplers (DoGS) offer customized variable selection orders for a given sampling budget and...

We apply the method of "blocking Gibbs" sampling to a problem of great importance and complexity-linkage analysis. Blocking Gibbs sampling combines exact local computations with Gibbs sampling, in a way that complements the strengths of both. The method is able to handle problems with very high complexity, such as linkage analysis in large pedigrees with many loops, a task that no other known m...

Abstract. The Heisenberg group is one of the simplest sub-Riemannian settings in which we can define non-elliptic Hörmander type generators. We can then consider coercive inequalities associated to such generators. We prove that a certain class of nontrivial Gibbs measures with quadratic interaction potential on an infinite product of Heisenberg groups satisfy logarithmic Sobolev inequalities.

We propose a Gibbs sampling algorithm to detect additive outliers and patches of outliers in bilinear time series models based on Bayesian view. We first derive the conditional posterior distributions, and then use the results of first Gibbs run to start the second adaptive Gibbs sampling. It is shown that our procedure could reduce possible effects on masking and swamping. At last, some simula...

This paper proposes a procedure to detect patches of outliers in an autoregressive process. The procedure is an improvement over the existing detection methods via Gibbs sampling. We show that the standard outlier detection via Gibbs sampling may be extremely ine cient in the presence of severe masking and swamping e ects. The new procedure identi es the beginning and end of possible outlier pa...

1 Models 2 1.1 Matrix factorisation models . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Matrix factorisation with ARD and importance values . . . . . . . . . . . . . 8 1.3 Hybrid matrix factorisation model . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.1 Model definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.2 Gibbs sampler . . . . . . . . . ....

The paper and presentation will focus on MCMC methods, implemented together in MC2Pack, an ox package which allows you to run a range of sampling algorithm (MH, Gibbs, Griddy Gibbs, Adaptive Polar Importance Sampling, Adaptive Polar Sampling, and Adaptive Rejection Metropolis Sampling) on a given posterior. Computation of the marginal likelihood for the model is also done automatically, allowin...

In many applications there is interest in representing both probabilistic and deterministic dependencies. This is especially the case in applications using Description Logics (DLs), where ontology engineering usually is based on strict knowledge, while there is also the need to represent uncertainty. We introduce a Markovian style of probabilistic reasoning in first-order logic known as Markov ...