Bayesian Poisson process partition calculus with an application to Bayesian L\'evy moving averages

This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailor-made to address inferential questions arising in a wide range of Bayesian nonparametric and spatial statistical models. The Poisson disintegration method is based on the formal statement of two results concerning a Laplace functional change of measure and a Poisson Palm/Fubini calculus in terms of random partitions of the integers {1,...,n}. The techniques are analogous to, but much more general than, techniques for the Dirichlet process and weighted gamma process developed in [Ann. Statist. 12 (1984) 351-357] and [Ann. Inst. Statist. Math. 41 (1989) 227-245]. In order to illustrate the flexibility of the approach, large classes of random probability measures and random hazards or intensities which can be expressed as functionals of Poisson random measures are described. We describe a unified posterior analysis of classes of discrete random probability which identifies and exploits features common to all these models. The analysis circumvents many of the difficult issues involved in Bayesian nonparametric calculus, including a combinatorial component. This allows one to focus on the unique features of each process which are characterized via real valued functions h. The applicability of the technique is further illustrated by obtaining explicit posterior expressions for L\'evy-Cox moving average processes within the general setting of multiplicative intensity models.Comment: Published at http://dx.doi.org/10.1214/009053605000000336 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Decision Fusion with Unknown Sensor Detection Probability

In this correspondence we study the problem of channel-aware decision fusion when the sensor detection probability is not known at the decision fusion center. Several alternatives proposed in the literature are compared and new fusion rules (namely 'ideal sensors' and 'locally-optimum detection') are proposed, showing attractive performance and linear complexity. Simulations are provided to compare the performance of the aforementioned rules.Comment: To appear in IEEE Signal Processing Letter

Effective Field Theories in Nuclear Particle and Atomic Physics

These are the proceedings of the workshop on ``Effective Field Theories in Nuclear, Particle and Atomic Physics'' held at the Physikzentrum Bad Honnef of the Deutsche Physikalische Gesellschaft, Bad Honnef, Germany from December 13 to 17, 2005. The workshop concentrated on Effective Field Theory in many contexts. A first part was concerned with Chiral Perturbation Theory in its various settings and explored strongly its use in relation with lattice QCD. The second part consisted of progress in effective field theories in systems with one, two or more nucleons as well as atomic physics. Included are a short contribution per talk.Comment: 56 pages, mini proceedings of the 337. WE-Heraeus-Seminar "Effective Field Theories in Nuclear Particle and Atomic Physics," Physikzentrum Bad Honnef, Bad Honnef, Germany, December 13 -- 17, 200

Cycle-based Cluster Variational Method for Direct and Inverse Inference

We elaborate on the idea that loop corrections to belief propagation could be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define region in a generalized belief propagation setting. The region graph is specified in such a way as to avoid dual loops as much as possible, by discarding redundant Lagrange multipliers, in order to facilitate the convergence, while avoiding instabilities associated to minimal factor graph construction. We end up with a two-level algorithm, where a belief propagation algorithm is run alternatively at the level of each cycle and at the inter-region level. The inverse problem of finding the couplings of a Markov random field from empirical covariances can be addressed region wise. It turns out that this can be done efficiently in particular in the Ising context, where fixed point equations can be derived along with a one-parameter log likelihood function to minimize. Numerical experiments confirm the effectiveness of these considerations both for the direct and inverse MRF inference.Comment: 47 pages, 16 figure