Tittles and abstracts:

Miguel Abadi, IME-USP

Clustering indexes in Extreme Value Theory

The observations of extremal events in a time serie is known to present a dicotomic

behaviour, depending on the nature ob the phenomena and the properties of the process: either

a close to Poisson process either a compound one. We describe different indexes and distribution which describe the clustering phenomena in the second case

Wagner Barreto-Souza, UFMG

Semiparametric generalized exponential frailty model for clustered survival data (with Vinícius D. Mayrink)

In this work, we propose a novel and mathematically tractable frailty model for clustered survival data by assuming a generalized exponential (GE) distribution for the latent frailty effect. Both parametric and semiparametric versions of the GE frailty model are studied with main focus for the semiparametric case, where an EM-algorithm is proposed. Our EM-based estimation for the GE frailty model is simpler, faster and immune to a flat likelihood issue affecting, for example, the semiparametric gamma model, as illustrated in this paper through simulated and real data. We also show that the GE model is at least competitive with respect to the gamma frailty model under misspecification. A broad analysis is developed, with simulation results explored via Monte Carlo replications, to evaluate and compare models. A real application using a clustered kidney catheter data is considered to demonstrate the potential for practice of the GE frailty model.

Bernardo Borba de Andrade, UNB

Analyzing Count Data with the Touchard Model

This talk presents modeling tools for analyzing count data with the Touchard distribution. The Touchard distribution has been recently proposed as a simple alternative to the Poisson with the ability to model both over and underdispersion in addition to allowing (mild) excess of zeroes. The Poisson is model is a special case of the Touchard. We provide an overview of properties and comparisons with the Poisson (with dispersion) and the Negative Binomial. Regression tools including diagnostics are also discussed. A beta version of an R package is presented.

Aline Duarte, IME-USP

Estimating the interaction graph of stochastic neural dynamics

In this seminar we present a stochastic model for a system of interacting neurons and address the question of statistical model selection for this class of stochastic models. More preciselly, each neuron will be modeled as a chains with memory of variable length. The relationship between a neuron and its pre and postsynaptic neurons defines an oriented graph, the interaction graph of the model. In this seminar we present a consistent procedure to estimate this graph based on the observation of the spike activity of a finite set of neurons over a finite time.

Leandro Martins Cioletti, UNB

A Variational Principle for Specific Entropy and the Existence and Uniqueness problem of Gibbs Measures

The variational problem characterizing the Gibbsian probability measures associated to a continuous potential is a central one in

Probability and Ergodic Theory. The uniqueness of its solutions still is a widely open problem in these areas and have attracted,

for more than fifty years, the attention of several researchers in Probability Theory, Spectral Theory, Symbolic Dynamical Systems and Statistical Mechanics.

In this seminar we will present a variational formulation for the Specific Entropy (related to relative entropy and Kullback-Liebler divergence) of a

invariant or stationary measure and show how we can use the Theory of DLR-Gibbs measures and Martingale Theory to prove the existence and uniqueness of the solution

of the variational problem associated to a Hölder potential defined on a general metric compact space. We explain how some problems in Symbolic Dynamics

can be related to Markov Processes (and generalizations) on compact metric state spaces and how to obtain results like Central Limit Theorem and

Large Deviation using spectral properties of some positive operators that appears naturally in Symbolic Dynamics and Statistical Mechanics.

Fábio Prates Machado, IME-USP

Dispersão como estratégia de sobrevivência

Consideramos modelos de crescimento estocástico para representar uma espécie sujeita

a catástrofes. Analisamos a dispersão da população como possı́vel estratégia para a sobrevivência

da espécie. Neste trabalho mostramos que a resposta a esta questão depende fortemente dos efeitos

que um evento catastrófico teria sobre colônia de indivı́duos, das possı́veis restrições espaciais do

ambiente e da probabilidade que cada indivı́duo tem de sobrevivência, quando exposto a um novo

desastre.

Lucas Moreira, UNB

Stochastically perturbed chains of variable memory

In this paper, we study inference for chains of variable order under two distinct contamination regimes. Consider we have a chain of variable memory on a finite

alphabet containing zero. At each instant of time an independent coin is flipped and if it turns head a contamination occurs. In the first regime a zero is read independent

of the value of the chain. In the second regime, the value of another chain of variable memory is observed instead of the original one. Our results state that the difference

between the transition probabilities of the original process and the corresponding ones of the contaminated process may be bounded above uniformly. Moreover, if the

contamination probability is small enough, using a version of the Context algorithm we are able to recover the context tree of the original process through a contaminated

sample. In addition, we propose weather models to predict the possibility of the next day being hot or not, given the information of maximum temperatures of the previous days

in the Federal District.

Rosangela Helena Loschi, UFMG

The challenge of Modeling Underreported Data (Joint work with: Guilherme L. de Oliveira and Renato M. Assunção)

A major challenge when monitoring risks in socially deprived areas, is that economic, epidemiological and social data are typically underreported. To deal with this problem, counts in suspected areas are usually approached as censored information. The censored Poisson model (CPM), used to model underreported counts, assumes that all censored areas must be precisely known a prior, which is not a reasonable assumption in most practical situations. We develop a new model that describes the joint behavior of the observed data and the data reporting process. We propose a random mechanism to specify the censored (underreported) regions thus introducing a random censoring Poisson model (RCPM). Assuming the proposed model, we are able to estimate both the censoring probability and the relative risk for the event of interest in each region. We elicit different prior distributions for the censoring probabilities. The main focus is to infer about the relative risks and about the censoring indicator latent variables. Despite obtaining full conditional distributions with closed form, the Gibbs sampler shows to be an inefficient algorithm to sample from the posteriors. We develop an MCMC algorithm to sample from the posterior distribution. The algorithm relies on the data augmentation strategy (Tanner&Wong,1987, Chib1992) simplifying substantially the posterior sampling. We run a simulation study evaluating the proposed algorithm and comparing the proposed model and the CPM in different scenarios. We perform a sensitivity analysis by eliciting different prior distributions for the censoring probabilities in RCPM, and by fixing different censoring criteria in CPM. We apply the proposed model to account for potential underreporting in the early neonatal mortality counts in regions of Minas Gerais State, Brazil, in which data quality is known to be truly poor.

Alexandre Galvão Patriota, IME-USP

Modelos de regressão com parametrização geral

Nesta palestra eu apresentarei o modelo de regressão com parametrização geral e os principais resultados desenvolvidos até o momento. Este modelo unifica uma gama de modelos estatísticos tais como modelos mistos, modelos não lineares, modelos com erros nas variáveis, modelos heteroscedásticos, entre outros.

Pablo Martin Rodriguez, ICMC-USP

The accessibility percolation model on trees

We consider the accessibility percolation model on trees. For each vertex of a graph we associate an absolutely continuous random variable coming from an i.i.d. sequence of random variables. We say that two vertices are connected through an accessible path if the random variables related to the unique path connecting these vertices are in increasing order. An issue of interest is the existence of an infinite accessible path, event called as accessibility percolation in the scientific literature. In this talk we will discuss about the motivation and formulation of this model, and we will show recent results about the phase transition for this model on some families of trees.

(em português) O modelo de percolação acessível em árvores

Consideramos o modelo de percolação acessível em árvores. Para cada vértice do grafo é associada uma variável aleatória absolutamente continua, tomada de uma sequência de variáveis i.i.d. Dizemos que dois vértices estão conectados a través de um caminho acessível se as respectivas variáveis aleatórias do único caminho que os conecta estão em ordem crescente. O interesse é na existência de um caminho acessível infinito, evento que chamamos de percolação acessível. Neste seminário iremos discutir sobre a motivação e formulação inicial deste modelo e iremos apresentar os resultados recentes de transição de fase em diferentes tipos de árvores.

Vera Tomazella, UFSCar

Competing risks modeling for repairable systems: An objective Bayesian approach

The focus of this work is on the analysis of repairable system subject to several failure modes. We present a Bayesian approach under an overall reference prior for the parameters of the Power law process intensities under competing risks. An orthogonal reparametrization is used to obtain an objective Bayesian prior which is invariant under relabelling of the failure modes. The resulting posterior is a product of gamma distributions and has appealing properties: one-to-one invariance, consistent marginalization and consistent sampling properties. Moreover, the resulting Bayes estimators have closed-form expressions and are naturally unbiased for all the parameters of the model. The methodology is applied in the analysis of records of automotive warranty claims and simulation study was carried out to study the efficiency of the methods proposed.

Filidor Edilfonso Vilca Labra, UNICAMP

Linear Mixed Models using Skew-Normal/Independent Distributions: Estimation and Influence analysis

The linear mixed models is discussed under skew-normal/independent distribution. This class provides a useful generalization of normal (and skew-normal)linear mixed models since it is assumed that the random effects and the random error terms follow jointly a multivariate skewnormal/independent distribution. Inspired by the EM algorithm that is used to obtain the maximum likelihood estimates, a study influence analysis for linear mixed models is developed, following the approach of Zhu et al. (2001) and Zhu and Lees (2001). The influence of observations on statistical inference is of importance in statistical data analysis. A practical and well-established approach to influence analysis is based on case deletion (Zhu et al., 2001), a general approach was proposed by Cook (1986) and Zhu and Lee (2001), that is well-known as the local influence method. Finally, a real data set has been analyzed in order to illustrate the usefulness of the proposed methodology.