25 Novembro 2016, 15:09 • Ana Maria Santos Ferreira Gorjão Henriques
Modelling extremal temporal dependence in stationary time series
Alexandra Ramos (Faculdade de Economia da Universidade do Porto)
December 13 (Tue.), 11:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)
Extreme value theory concerns the statistical study of the extremal properties of random processes. The most common problems treated by extreme value methods involve modeling the tail of an unknown distribution function from a set of observed data with the purpose of quantifying the frequency and severity of events more extreme than any that have been observed previously. A fundamental issue in applied multivariate extreme value (MEV) analysis is modelling dependence within joint tail regions. In this seminar we suggest modelling joint tails of the distribution of two consecutive pairs (Xi;Xi+1) of a first-order stationary Markov chain by a dependence model described in Ramos and Ledford (2009). Applications of this modelling approach to real data are then considered.
Ramos and Ledford (2009). A new class of models for bivariate joint tails. J. R. Statist. Soc., B. 71. p. 219-241.
16 Novembro 2016, 19:39 • Ana Maria Santos Ferreira Gorjão Henriques
Binary autoregressive geometric modelling in a DNA context
Sónia Gouveia (Institute of Electronics and Informatics Engineering and Centre for R&D in Mathematics and Applications, University of Aveiro, Portugal)
November 22 (Tue.), 11:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)
Symbolic sequences occur in many contexts and can be characterized e.g. by integer-valued intersymbol distances or binary-valued indicator sequences. The analysis of these numerical sequences often sheds light on the properties of the original symbolic sequences. This talk introduces new statistical tools to explore the autocorrelation structure in indicator sequences and to evaluate its impact on the probability distribution of intersymbol distances. The methods are illustrated with data extracted from mitochondrial DNA sequences.
This is a joint work with Manuel Scotto (IST, Lisbon, Portugal), Christian Weiss (Helmut Schmidt University, Hamburg, Germany) and Paulo Ferreira (DETI, IEETA, Aveiro, Portugal).
25 Outubro 2016, 18:29 • Ana Maria Santos Ferreira Gorjão Henriques
On the peaks-over-threshold method in extreme value theoryLaurens de Haan (Erasmus University Rotterdam and Centro de Estatística e Aplicações da UL)
November 8 (Tue.), 11:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)
The origin, the development and the use of the peaks-over-threshold method (in particular in higher-dimensional spaces) will be discussed as well as some issues that need clarification.
11 Outubro 2016, 17:24 • Ana Maria Santos Ferreira Gorjão Henriques
Spatial and Spatio-Temporal Nonlinear Time Series
Wolfgang Schmid (European University, Frankfurt (Oder), Germany)
October 25 (Tue.), 11:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)
In this talk we present a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model. We show additionally how the introduced spatial ARCH model can be used in spatiotemporal settings. In contrast to the temporal ARCH model, in which the distribution is known given the full information set of the prior periods, the distribution is not straightforward in the spatial and spatiotemporal setting. However, it is possible to estimate the parameters of the model using the maximum-likelihood approach. Via Monte Carlo simulations, we demonstrate the performance of the estimator for a specific spatial weighting matrix. Moreover, we combine the known spatial autoregressive model with the spatial ARCH model assuming heteroscedastic errors. Eventually, the proposed autoregressive process is illustrated using an empirical example. Specifically, we model lung cancer mortality in 3108 U.S. counties and compare the introduced model with two benchmark approaches.
(joint work with Robert Gartho and Philipp Otto)
5 Outubro 2016, 13:38 • Ana Maria Santos Ferreira Gorjão Henriques
Distributed and robust network localization
Cláudia Soares (ISR, Lisbon)
October 11 (Tue.), 11:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)
Signal processing over networks has been a broad and hot topic in the last few years. In most applications networks of agents typically rely on known node positions, even if the main goal of the network is not localization. Also, mobile agents need localization for, e.g., motion planning, or formation control, where GPS might not be an option. Also, real-world conditions imply noisy environments, and the network real-time operation calls for fast and reliable estimation of the agents’ locations. So, galvanized by the compelling applications researchers have dedicated a great amount of work to finding the nodes in networks. With the growing network sizes of devices constrained in energy expenditure and computation power, the need for simple, fast, and distributed algorithms for network localization spurred this work. Here, we approach the problem starting from minimal data collection, aggregating only range measurements and a few landmark positions. We explore tailored solutions recurring to the optimization and probability tools that can leverage performance under noisy and unstructured environments. Thus, the contributions are, mainly:
• Distributed localization algorithms characterized for their simplicity but also strong guarantees;
• Analyses of convergence, iteration complexity, and optimality bounds for the designed procedures;
• Novel majorization approaches which are tailored to the specific problem structure.