Research Seminar in Probability and Statistics II - #11

19 Maio 2016, 10:58 Manuel Cabral Morais

The Block Maxima and POT methods and, an extension of POT to integrated stochastic processes

Ana Ferreira (DM-IST; CEAUL & CEMAT)

May 25 (Wed.), 16:00 - Room 4.35 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)

We shall review the classical maximum domain of attraction condition underlying BM and POT, two fundamental methods in Extreme Value Theory. A theoretical comparison between the methods will be presented.

Afterwards, the maximum domain of attraction condition to spatial context will be discussed. Then a POT-type result for the integral of a stochastic process verifying the maximum domain of attraction condition will be obtained.

Research Seminar in Probability and Statistics II - #10

7 Maio 2016, 10:09 Manuel Cabral Morais

I) Statistical Applications in Climatology. II) Predicting the weather for the next week, outlook of the climate for the XXIst century

I) Vanda Pires. II) Pedro Viterbo (IPMA, Instituto Português do Mar e da Atmosfera)

May 18 (Wed.), 16:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)

I) The study of Climatology is based on the analysis and interpretation of weather data collected over many years. To analyze such data, knowledge of basic techniques and statistical methods is required. The climate analysis uses principles and techniques of meteorological analysis, numerical and statistical. 

Applied climatology makes the maximum use of meteorological and climatological knowledge and information for solving practical social, economic, and environmental problems. 

Assessments of the effects of climate variability and climate change on human activities, as well as the effects of human activities on climate, are major factors in local, national, and global economic development,  social programmes, and resource management.

The main focus of this presentation is to show statistical applications in climatology that are used at IPMA, for example, climatic normals, climatic indicators, trends, return periods and others.

II) Current state of the art of weather forecasts has skill until day 6 to day 8. Nevertheless, it is possible to have reliable evolutions of the climate of the XXIst century; this apparent paradox will be explained in the presentation. Scenarios for the evolution of greenhouse gases throughout the century will be reviewed, as well as the climate impacts of each scenario. A climate portal (, or is being finalized: a rich source of information for students, research, private and public sector, especially designed for guiding multi-decadal strategic decisions.

Research Seminar in Probability and Statistics II - #9

4 Maio 2016, 17:03 Manuel Cabral Morais

On Eigenvalues of the Transition Matrix of some Count Data Markov Chains

Christian Weiss (Dept. of Mathematics and Statistics, Helmut Schmidt Universität)

May 11 (Wed.), 16:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)

A stationary Markov chain is uniquely determined by its transition matrix, the eigenvalues of which play an important role for characterizing the stochastic properties of a Markov chain. Here, we consider the case where the monitored observations are counts, i.e., having values in either the full set of non-negative integers, or in a finite set of the form {0,...,n} with a prespecified upper bound n. Examples of count data time series as well as a brief survey of some basic count data time series models is provided.

Then we analyze the eigenstructure of count data Markov chains. Our main focus is on so-called CLAR(1) models, which are characterized by having a linear conditional mean, and also on the case of a finite range, where the second largest eigenvalue determines the speed of convergence of the forecasting distributions. We derive a lower bound for the second largest eigenvalue, which often (but not always) even equals this eigenvalue. This becomes clear by deriving the complete set of eigenvalues for several specific cases of CLAR(1) models. Our method relies on the computation of appropriate conditional (factorial) moments.

Research Seminar in Probability and Statistics II - #8

27 Abril 2016, 13:12 Manuel Cabral Morais

From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification

André Martins (Unbabel and Instituto de Telecomunicações)

May 4 (Wed.), 16:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)

The softmax transformation is a key component of several statistical learning models, encompassing multinomial logistic regression, action selection in reinforcement learning, and neural networks for multi-class classification. Recently, it has also been used to design attention mechanisms in neural networks, with important achievements in machine translation, image caption generation, speech recognition, and various tasks in natural language understanding and computation learning. In this talk, I will describe sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, I will show how its Jacobian can be efficiently computed, enabling its use in a neural network trained with backpropagation. Then, I will propose a new smooth and convex loss function which is the sparsemax analogue of the logistic loss. An unexpected connection between this new loss and the Huber classification loss will be revealed. We obtained promising empirical results in multi-label classification problems and in attention-based neural networks for natural language inference. For the latter, we achieved a similar performance as the traditional softmax, but with a selective, more compact, attention focus.

Research Seminar in Probability and Statistics II - #7

19 Abril 2016, 09:19 Manuel Cabral Morais

Geostatistical History Matching with Ensemble Updating

Maria João Quintão (CERENA, IST, Univ. de Lisboa)

April 27 (Wed.), 16:00 - Room P3.10 (Math. Building, IST, Av. Rovisco Pais, 1049-001 Lisboa)

In this work, a new history matching methodology is proposed, coupling within the same framework the advantages of using geostatistical sequential simulation and the principles of ensemble Kalman filters: history matching based on ensemble updating.  The main idea of this procedure is to use simultaneously the relationship between the petrophysical properties of interest and the dynamical results to update the static properties at each iteration, and to define areas of influence for each well. This relation is established through the experimental non-stationary covariances, computed from the ensemble of realizations. A set of petrophysical properties of interest is generated through stochastic sequential simulation. For each simulated model, we obtain its dynamic responses at the wells locations by running a fluid flow simulator over each single model. Considering the normalized absolute deviation between the dynamic responses and the real

dynamic response in each well as state variables, we compute the correlation coefficients of the deviations with each grid cell through the ensemble of realizations. Areas of high correlation coefficients are those where the permeability is more likely to play a key role for the production of that given well. Using a local estimation of the response of the deviations, through a simple kriging process, we update the subsurface property of interest at a given localization.