Pseudolikelihood inference for Gibbsian T-tessellations ... and point processes

Recently a new class of planar tessellations, named T-tessellations, was introduced. Splits, merges and a third local modification named flip where shown to be sufficient for exploring the space of T-tessellations. Based on these local transformations and by analogy with point process theory, tools Campbell measures and a general simulation algorithm of Metropolis-Hastings-Green type were translated for random T-tessellations.The current report is concerned with parametric inference for Gibbs models of T-tessellations. The estimation criterion referred to as the pseudolikelihood is derived from Campbell measures of random T-tessellations and the Kullback-Leibler divergence. A detailed algorithm for approximating the pseudolikelihood maximum is provided. A simulation study seems to show that bias and variability of the pseudolikelihood maximum decrease when the tessellated domain grows in size.In the last part of the report, it is shown that an analogous approach based on the Campbell measure and the KL divergence when applied to point processes leads to the well-known pseudo-likelihood introduced by Besag. More surprisingly, the binomial regression method recently proposed by Baddeley and his co-authors for computing the pseudolikelihood maximum can be derived using the same approach starting from a slight modification of the Campbell measure

Guessing under source uncertainty

This paper considers the problem of guessing the realization of a finite alphabet source when some side information is provided. The only knowledge the guesser has about the source and the correlated side information is that the joint source is one among a family. A notion of redundancy is first defined and a new divergence quantity that measures this redundancy is identified. This divergence quantity shares the Pythagorean property with the Kullback-Leibler divergence. Good guessing strategies that minimize the supremum redundancy (over the family) are then identified. The min-sup value measures the richness of the uncertainty set. The min-sup redundancies for two examples - the families of discrete memoryless sources and finite-state arbitrarily varying sources - are then determined.Comment: 27 pages, submitted to IEEE Transactions on Information Theory, March 2006, revised September 2006, contains minor modifications and restructuring based on reviewers' comment

Using proper divergence functions to evaluate climate models

It has been argued persuasively that, in order to evaluate climate models, the probability distributions of model output need to be compared to the corresponding empirical distributions of observed data. Distance measures between probability distributions, also called divergence functions, can be used for this purpose. We contend that divergence functions ought to be proper, in the sense that acting on modelers' true beliefs is an optimal strategy. Score divergences that derive from proper scoring rules are proper, with the integrated quadratic distance and the Kullback-Leibler divergence being particularly attractive choices. Other commonly used divergences fail to be proper. In an illustration, we evaluate and rank simulations from fifteen climate models for temperature extremes in a comparison to re-analysis data

Empirical and Strong Coordination via Soft Covering with Polar Codes

We design polar codes for empirical coordination and strong coordination in two-node networks. Our constructions hinge on the fact that polar codes enable explicit low-complexity schemes for soft covering. We leverage this property to propose explicit and low-complexity coding schemes that achieve the capacity regions of both empirical coordination and strong coordination for sequences of actions taking value in an alphabet of prime cardinality. Our results improve previously known polar coding schemes, which (i) were restricted to uniform distributions and to actions obtained via binary symmetric channels for strong coordination, (ii) required a non-negligible amount of common randomness for empirical coordination, and (iii) assumed that the simulation of discrete memoryless channels could be perfectly implemented. As a by-product of our results, we obtain a polar coding scheme that achieves channel resolvability for an arbitrary discrete memoryless channel whose input alphabet has prime cardinality.Comment: 14 pages, two-column, 5 figures, accepted to IEEE Transactions on Information Theor

Multiscale autocorrelation function: a new approach to anisotropy studies

We present a novel catalog-independent method, based on a scale dependent approach, to detect anisotropy signatures in the arrival direction distribution of the ultra highest energy cosmic rays (UHECR). The method provides a good discrimination power for both large and small data sets, even in presence of strong contaminating isotropic background. We present some applications to simulated data sets of events corresponding to plausible scenarios for charged particles detected by world-wide surface detector-based observatories, in the last decades.Comment: 18 pages, 9 figure