Title: Enhancing the Performance of the Likelihood Ratio Test for Small and Moderate Samples

Abstract: NThe likelihood ratio (LR) test is the ultimate statistical tool for evaluating two competing point hypotheses based on observed data, with a wide range of applications. Although the LR test offers numerous advantages in several contexts, it faces important limitations mainly because its application depends on knowing the true distribution of the LR statistic, which is usually difficult to determine. The most common alternative is to approximate this distribution with a chi-squared distribution, but this may lead to inaccurate inferences, specially when the sample size is small. The objective of this paper is to develop a strategy for improving the LR test for small and moderate size samples. For this, we introduce the chi-squared inf distribution as a “tail-corrected” version of the chi-squared distribution, obtained by introducing a correction parameter in the reference distribution. Although asymptotically equivalent to the classical LR test, our proposed approach yields more accurate p−values, while eliminating the need for complex Bartlett and Bartlett-type corrections and avoiding the computational burden associated with bootstrap-based methods. We evaluate the method’s performance through extensive Monte Carlo simulations and illustrate its practical advantages using two real datasets.

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: 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.

Title: A Frailty models for complex repairable systems reliability under imperfect repair assumption

Abstract: Repairable systems are often used to model the reliability of restored components after a failure is observed. This work presents reliability models for repairable systems subject to successive failures and imperfect repair actions, incorporating frailty terms to capture unobserved heterogeneity. The modeling framework is based on ARA(m) and ARI(m) structures combined with power law processes and Gamma-distributed frailties. This approach allows for a more realistic description of industrial systems, such as sugarcane harvesters, by accounting for both cumulative degradation and latent variability between units. Simulation studies and real-data applications demonstrate the models' predictive performance and practical potential in reliability planning and maintenance strategies.