Ciclo de Palestras – Segundo Semestre de 2025

As palestras ocorrem de forma presencial às quartas-feiras às 15h30 na sala I-044-B, a menos de algumas exceções devidamente indicadas.

 In this talk, I will present recent advances on Bayesian Inference under models mis-specification. We focus on a multilevel data generating process and discuss the estimation of populational level parameters. We provide a theoretical justification for the proposed method in terms of exchangeable and partially exchangeable sequences. Simulation studies indicate that the proposed approach has good frequentist properties when data generating process and proposed model induces a partially exchangeable sequence associated with the unknown quantity of interest.

The stochastic volatility-in-mean (SVM) model is revisited. Our methodology incorporates heavy tails and requires less computational time in simulations and estimation compared with other approaches proposed in the literature for Bayesian inference. We approximate the likelihood function of the model by applying Hidden Markov Model techniques, which makes Bayesian inference feasible in real time. We draw samples from the posterior distribution of the parameters using importance sampling, with a multivariate normal distribution whose mean and covariance matrix are given by the posterior mode and the inverse of the Hessian matrix evaluated at this mode. Furthermore, the frequentist properties of the estimators are analyzed through a simulation study. Finally, we provide empirical evidence by estimating the SVM model using daily data from the S&P, NIKKEI 225, DAX 30, and MEXBOL indexes.

Local: IMPA, Auditório 1 — Estrada Dona Castorina, 110, Jardim Botânico
14:00 – Marcelo Soares Campos (IMPA)
 
O processo triângulo-livre modificado e novas cotas inferiores para $R(3,k)$
O número de Ramsey $R(3,k)$ é o maior $n$ tal que existe um grafo sem triângulos com $n$ vértices e número de independência menor que $k$. O processo triângulo livre forma um grafo triângulo livre aleatório adicionando uma aresta escolhida uniformemente ao acaso por vez, dentre as arestas que não formam um triângulo com as já adicionadas. Bohman e Keevash e Fiz-Pontiveros, Griffiths e Morris analisaram o processo triângulo livre até o final e dessa forma demonstraram que $R(3,k)\geq \frac$. Nessa palestra vou apresentar uma modificação do processo triângulo livre que utilizamos para mostrar que $R(3,k)\geq \frac$, disprovando uma conjectura de Fiz-Pontiveros, Griffiths e Morris.
 
15:20 – 15:40 – café
 
15:40 – Max Oliveira de Souza (UFF)
 
Gradient flows of discrete and continuous evolutionary models
We will present an unified "energetic" view of three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenerated Fokker-Planck Diffusion; (iii) the Replicator Equation, a paradigm in Evolutionary Game Theory. It is well known that the Replicator Dynamics for two strategies is a gradient flow with respect to the celebrated Shahshahani distance. We will discuss how to reformulate the Moran process and the Kimura Equation as gradient flows, and show that the associated gradient flows are compatible in an appropriate sense.
17:00 a 17:40 – discussão e lanche

Dengue is a vector-borne disease and a major public health concern in Brazil. Its continuing and rising burden has led the Brazilian Ministry of Health to request for modelling efforts to aid in the preparedness and response to the disease. In this scope, predicting the number of cases is essential for an appropriate decision making process in order to reduce or avoid a higher burden caused by the disease. In this seminar I will present the dengue and its characteristics and why it is not an easy task to forecast the number of cases. I will present some short term predictive models to “nowcast” the actual number of cases for early-warning systems and also an one-year-ahead forecasting model to be used either as a preview for the next year and/or probabilistic epidemic bands for dengue cases in the country.

Padrões de pontos frequentemente exibem mudanças abruptas, hotspots e dependência espacial que varia com a intensidade local. No contexto de processos de Poisson, esses aspectos correspondem a descontinuidades e não-estacionariedade na função de intensidade, difíceis de capturar por modelos tradicionais. Esta tese propõe um processo de Cox espacial onde a não-estacionariedade é induzida por uma partição aleatória do espaço, via tesselação de Voronoi. Essa construção permite transições bruscas e heterogeneidade espacial, além de reduzir o custo computacional. Um algoritmo MCMC livre de discretização é desenvolvido, garantindo inferência exata. A metodologia é avaliada em exemplos sintéticos e reais. Na análise de queimadas no Mato Grosso, os resultados revelam que as regiões do estado com os maiores riscos se concentram ao norte, área de desmatamento e de expansão agrícola. O modelo demonstra flexibilidade, escalabilidade e capacidade de capturar estruturas espaciais complexas.

Eventos extremos de precipitação representam um desafio significativo para regiões vulneráveis, como o estado do Maranhão, marcado por forte sazonalidade e alta variabilidade climática. O índice Rnnmm, que contabiliza o número de dias em que a precipitação diária ultrapassa um determinado limiar (como o R20mm), é amplamente utilizado para caracterizar esses extremos. Contudo, sua modelagem estatística enfrenta limitações, especialmente diante da influência irregular de fenômenos de grande escala, como El Niño e La Niña, e da tendência de ocorrência em sequência dos eventos extremos. Neste trabalho, propomos um modelo espaço-temporal baseado em processos de Hawkes, combinando uma intensidade de base Weibull para capturar a sazonalidade e efeitos de longo prazo, com um núcleo de excitação exponencial para representar o agrupamento de dias extremos. A dependência espacial é introduzida por meio de Processos Gaussianos aplicados aos parâmetros, e a estimação é realizada em um arcabouço Bayesiano via MCMC, permitindo interpolação em locais sem observações. A aplicação ao índice R20mm no Maranhão (2013–2022) demonstra que o modelo proposto fornece uma representação mais realista da dinâmica espaço-temporal de eventos extremos, contribuindo para uma compreensão mais refinada de padrões regionais de precipitação e oferecendo subsídios para estratégias de mitigação e adaptação às mudanças climáticas.

The traditional estimation of mixture regression models is based on the assumption of component normality (or symmetry), making it sensitive to outliers, heavy-tailed errors, and asymmetric errors. In this work, we propose addressing these issues simultaneously by considering a finite mixture of regression models with multivariate scale mixtures of skew-normal distributions. This approach provides greater flexibility in modeling data, accommodating both skewness and heavy tails. Additionally, the proposed model allows the use of a specific vector of regressors for each dependent variable. The main advantage of using the mixture of regression models under the class of multivariate scale mixtures of skew-normal distributions is their convenient hierarchical representation, which allows easy implementation of inference. We develop a simple expectation–maximization (EM) type algorithm to perform maximum likelihood inference for the parameters of the proposed model. The observed information matrix is derived analytically to calculate standard errors. Some simulation studies are also
presented to examine the robustness of this flexible model against outlying observations. Finally, a real dataset is analyzed, demonstrating the practical value of the proposed method. The R scripts implementing our methods are available on the GitHub repository at https://bit.ly/3CLcI1W.

BENITES, L.; LACHOS, V. H.; BOLFARINE, H.; ZELLER, CAMILA BORELLI.
Finite mixture of regression models based on multivariate scale mixtures of skew-
normal distributions. COMPUTATIONAL STATISTICS, p. 1-32, 2025.

Bernoulli factory MCMC algorithms implement accept-reject Markov chains without explicit computation of acceptance probabilities, and are used to target posterior distributions associated with intractable likelihood models. Intractable likelihoods naturally arise in continuous-time models and mixture distributions, or from the marginalisation of a tractable augmented model. Bernoulli factory MCMC algorithms often mix better than alternatives that target a tractable augmented posterior. However, for a likelihood that factorizes over observations, we show that their computational performance typically deteriorates exponentially with data size. To address this, we propose a simple divide-and-conquer Bernoulli factory MCMC algorithm and prove that it has polynomial complexity of degree between 1 and 2, with the exact degree depending on the existence of efficient unbiased estimators of the intractable likelihood ratio. We demonstrate the effectiveness of our approach with applications to Bayesian inference in two intractable likelihood models, and observe respective polynomial cost of degree 1.2 and 1 in the data size.

When quantiles are fitted separately, the resultant regression lines may cross, violating the basic probabilistic rule that quantiles are monotonic functions and possibly causing problems for inference and interpretation in practice. This article introduces a method for handling crossing issues regarding the analysis of complex survey data under informative sampling. Using the location-scale mixture representation of the asymmetric Laplace distribution, we write a joint posterior density function for the quantile levels of interest and develop a constrained Expectation-Maximization algorithm. A model-based simulation study is proposed, and data from the Brazilian National Demographic Health Survey of Women and Children is analyzed to verify and illustrate the algorithm’s effectiveness.

O processo de contato (clássico) busca modelar a evolução de uma doença infecciosa do seguinte modo: Indivíduos infectados transmitem a doença para seus vizinhos após tempos exponenciais de taxa λ > 0 e ficam curados após tempos exponenciais de taxa 1. Já o processo de contato sob renovações flexibiliza esse modelo, permitindo que os tempos entre possíveis curas tenham uma distribuição μ mais geral.  Nesta apresentação introduziremos esses processos e discutiremos sobre condições suficientes a respeito de μ para que o parâmetro crítico seja positivo e finito no processo de contato sob renovações. Trabalho em conjunto com Maria Eulalia Vares.

Time-dependent regionalization or spatially restricted grouping is an important field of research that has as the main goal to evaluate how spatial clusters evolve over time. In this work, regionalization problem will be treated probabilistically as a random partition of the map at each time and the sequence of spatial partitions will be time-dependent, allowing the temporal evolution of the clusters to be inferred. We assume a product partition prior for the random partition at each time. The temporal correlation between partitions is introduced through the temporal structure assumed for prior cohesions. We employ random spanning trees to facilitate the exploration of the partition search space and to guarantee spatially constrained clustering. This work is motivated by a relevant applied problem: identifying spatial and temporal patterns of mosquito-borne diseases. Given the overdispersion present in this type of data, we introduce a spatio-temporal Poisson mixture model in which mean and dispersion parameters vary according to spatio-temporal covariates. The proposed model is applied to analyze the number of dengue cases reported weekly from 2018 to 2023 in the Southeast region of Brazil. We also evaluate model performance using simulated data. The proposed model was competitive for analyzing the temporal evolution of spatial clustering. Joint work with: Jessica Pavani e Fernando A. Quintana.

We propose a non-stationary model constructed using a mixture of spatio-temporal covariance models with advection effects (Gupta and Waymire, 1987; Cox and Isham, 1988); namely, models that have larger covariance values along an orientation vector in the spatio-temporal index set, that simulate wind direction and cloud movement. We show that a mixture of such models can allow for wind direction change in data during (estimated) time intervals, unlike classical models that use rigid advection effects. We construct a MCMC procedure for Bayesian estimation, and illustrate the problem with rainfall data from the southeastern region of Brazil. This is a joint work with Pedro Nasevicius Ramos (UNICAMP).