Title: A Importância da Estatística para a Oncologia: Análise de Sobrevivência em Populações com Indivíduos Imunes

Abstract: A Estatística desempenha um papel relevante na oncologia ao fornecer ferramentas para a análise de dados de tempo até a ocorrência de eventos, como recidiva da doença ou óbito. A análise de sobrevivência constitui um dos principais campos teóricos para esse tipo de estudo, incorporando características como a censura, que ocorre quando o tempo exato do evento não é observado para todos os indivíduos, e a heterogeneidade populacional. Nesta apresentação, discutimos conceitos fundamentais da análise de sobrevivência, com ênfase em modelos estatísticos baseados em estruturas probabilísticas para populações que incluem indivíduos imunes ao evento de interesse, conhecidos como modelos de cura. Esses modelos permitem descrever distribuições de tempos de sobrevivência que admitem uma probabilidade positiva de não ocorrência do evento. O objetivo é destacar o papel da modelagem estatística na análise e interpretação de dados clínicos no contexto da oncologia.

Title: Teoria de Valores Extremos aplicados a estatísticas de jogadores de futebol das principais ligas européias

Abstract: A Premier League e a La Liga são duas das ligas de futebol mais tradicionais e competitivas do mundo, reunindo alguns dos melhores jogadores da história do esporte. Diante disso, o presente trabalho tem como objetivo principal aplicar os modelos de mistura para análise de valores extremos a fim de quantificar o alto desempenho dos jogadores em estatísticas individuais como gols, assistências e participações diretas a gols. Foram utilizadas as estatísticas das temporadas de 2009 a 2023, divididas em duas eras distintas: Era de Ouro (2009–2016) e Era Moderna (2017–2023). O estudo demonstra que os modelos MGPD foram eficazes na descrição das caudas superiores das distribuições, contribuindo para uma análise robusta e comparativa entre os desempenhos ao longo dos anos.

Palavras-Chave: Premier League, La Liga, Modelos de Mistura, Inferência Bayesiana, Valores Extremos.

Title: Estimating the number of hidden neurons in neural networks

Abstract: Neural Networks are among the most powerful models in statistical learning and artificial intelligence. The flexibility of this model depends on its architecture, that plays an essential role in its performance. Choosing the correct architecture of a Neural Network Model is a challenging problem. In this talk, I will present recent consistency results on model selection for Neural Network Models for the classification task. Ou approach is based on a penalized maximum likelihood estimator for the number of hidden nodes of a single hidden layer Neural Network. This is a joint work with Tiago Pereira Marques (USP) and Daniela Rodriguez (Universidad Di Tella / Conicet).

Title: Community detection on binary graphical models with mean-field interactions

Abstract: We consider a system of binary interacting chains describing the dynamics of a group of N individuals that, at each time unit, either send some signal to the others or remain silent otherwise. The interactions among the chains are encoded by a directed Erdös-Rényi random graph with unknown parameter 0<p<1. Moreover, the system is structured within two populations (excitatory chains versus inhibitory ones) which are coupled via a mean field interaction on the underlying Erdös-Rényi graph. These two populations are also unknown. In this talk, we will discuss a spectral method able to discriminate the excitatory chains from the inhibitory ones based only on the observation of the interacting chains over T time units. The results presented are based on a joint work Julien Chevallier (Grenoble, France).

Title: Modeling Sequential Data from Multiple Sources using Variable Length Markov Chains with Exogenous Covariates

Abstract: Variable Length Markov Chains with Exogenous Covariates (VLMCX) combine the flexibility of context-tree models with Generalized Linear Models to estimate transition probabilities. In this approach, the beta-context algorithm identifies the relevant past contexts and uses both the process history and time-dependent covariates to compute transition probabilities.

We extend this algorithm to include both time-varying and time-invariant covariates using multiple independent data sources, all modeled under a shared parameter structure and combined into a unified context tree. Our motivation is to investigate the impact of previous dengue rates, weather conditions, and socioeconomic factors on subsequent dengue rates across various municipalities in Brazil and districts in Rio de Janeiro, providing insights into dengue transmission dynamics. To incorporate spatial dependence, we include dengue cases from neighboring regions as exogenous covariates.

Ongoing work focuses on extending VLMCX to spatiotemporal settings while preserving temporal flexibility and improving the method by adding nonparametric components, handling missing data, and addressing low-frequency contexts.

This is joint work with Nancy Lopes Garcia (UNICAMP).

Title: Hydrodynamic limit of the symmetric zero-range process with slow boundary

Abstract: We study the hydrodynamic behavior of the symmetric zero-range process on the finite interval {1, …, N − 1} in contact with slow reservoirs at the boundary. Particles are injected and removed at sites 1 and N − 1 at rates that scale like N^(−θ), with θ ≥ 1. Under mild assumptions on the jump rate function and on the sequence of initial measures, we show that the empirical density evolves on the diffusive time scale according to a nonlinear heat equation, with boundary conditions that reflect the strength of the reservoirs.

Title: Unit ARMA-like models for bounded time series: an overview and the unit Gompertz ARMA case study

Abstract: Autoregressive moving average models with non-Gaussian components (ARMA-like models) provide a flexible framework for analyzing bounded time series. For random variables taking values in the standard unit interval, the so-called unit ARMA-like class has attracted increasing attention since the introduction of the beta autoregressive moving average model. Several extensions have been proposed by replacing the beta distribution with alternative unit distributions, enabling the modeling of conditional means, medians, or quantiles under serial dependence. This work presents an overview of the unit ARMA-like literature, summarizing the main modeling approaches and presenting a case study within this class of models: the unit Gompertz ARMA model for bounded time series. The proposed model exploits the closed-form quantile function of the unit Gompertz distribution, allowing a quantile-based parameterization with time-varying conditional quantiles driven by an ARMA structure.

Title: Time-varying dispersion integer-valued GARCH models for spatio-temporal counts

Abstract: Tuberculosis remains a major public health challenge in Brazil, exhibiting marked spatial heterogeneity and complex temporal dynamics. We analyse monthly tuberculosis counts from 61 municipalities in the state of São Paulo between 2001 and 2024 using a spatio-temporal INGARCH framework with time-varying dispersion. The proposed model, based on a multivariate negative binomial distribution, allows both the conditional mean and dispersion to evolve over time, while spatial dependence is captured through flexible weighting structures, including adjacency-based schemes and a MatÅLern correlation function. Simulation results show good finite-sample performance, and the application reveals heterogeneous space–time patterns and improved model fit.

Keywords: Tuberculosis; Spatio-temporal count data; INGARCH models; Time-varying dispersion; Spatial dependence; Negative binomial models.