Conferencias

Let f_i, i=1,...,n be a function on the integer that is observed with a Gaussian noise. When the variance of the noise is known, we construct the likelihood ratio test (LRT) for the null hypothesis "f is monotone increasing" with explicit calculation of the distribution of the statistic.
Our method is based on a "Steiner-like formula" that give the volume of a tube around the set of monotone increasing vectors of norm one. The test is generalized to the case where the variance is unknown. Some simulations show the performance and the robustness to non-normality.

TBA

TBA

We examine the stability of multi-dimensional state-dependent birth and death processes modeling multi-class queueing systems with the special feature that the service rates of the various classes depend on the number of users present of each of the classes.
As a result, the various classes interact in a complex dynamic fashion. Such models arise in several contexts, especially in wireless networks. The mathematical techniques employed, combine stochastic comparaisons, coupling and extended Lyapunov criteria.
Under certain monotonicity assumptions we provide an exact characterization of the stability region. The results are illustrated for simple examples of wireless networks with two or three interfering base stations.

We study some natural initial measures associated to selection of information.

We describe recent results obtained on the transient behaviour of some standard queues in a Markovian setting. Transient distributions of queueing systems such as the M/M/1 or the M/M/1/H models have been obtained long time ago.
After recalling these classic derivations and some more recent proposals, we present a new combinatorial approach based on a concept of duality proposed by Anderson, which allows to obtain new expressions of the transient distributions of these queues and of other models such as reset (also called queues with catastrophees).
This is joint work with A. Krinik, of CalPoly, Pomona, California, US.

We consider models for spatio-temporal processes which assume either non-negative values and often are observed as zero, or assume discrete values and are also inflated by zeros. Typically, in the first case, the spatial observations are obtained at fixed locations (point-referenced data) over a region D; whereas in the second, the region D is divided into a finite number of regular or irregular subregions (areal level) resulting on observations for each subregion. Our main idea is based on those of zero-inflated models, by assuming that the value observed at location or subregion s and time t, $y_t({\bf s})$, is a realization of a mixture between a Bernoulli distribution with a probability of success $\theta_t({\bf s})$ and a probability density function or probability function $p(y_t({\bf s}) \mid .)$.
For both, continuous and discrete cases, we include in the model, spatio-temporal latent processes to account for possible extra variation present in the mean structure of $\theta_t({\bf s})$ and/or of $p(y_t({\bf s}) \mid .)$. One of the main contributions lies in the fact that in the continuous case the observations are modelled in their original scale without the need of considering any transformation to attain normality of the data. Inference procedure is performed under the Bayesian paradigm. Markov Chain Monte Carlo methods are used to obtain samples from the target distribution and efficient sampling schemes are proposed. Our proposed model is applied for two different examples. In the context of point-referenced data we model the amount of rainfall over the city of Rio de Janeiro during 75 weeks; whereas in the areal data level case, we consider weekly cases of dengue fever in the city of Rio de Janeiro during the years of 2001-2002.