Título: Temporal dependence in sequences of spatial random partitions driven by spanning tree: An application to mosquito-borne diseases.
Palestrante: Rosangela Helena Loschi
Joint work with: Jessica Pavani e Fernando A. Quintana.
Resumo: 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.
Our next seminar will be held on Monday, November 10, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time). The meeting will take place at room C116- Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online.
Speaker: Luciana Silva Salgado (IM-UFRJ)
Title: Sensitivity and historic behavior for continuous maps on Baire metric spaces
Abstract:
Given a Baire metric space $(Y, d)$, a continuous map $T : Y \to Y$ and $\varphi$ a continuous bounded real valued function of $Y$, the set of $(T,\varphi)$-irregular points, also points with historic behavior, is formed by those points whose Cesàro average does not converge.
The Birkhoff's ergodic theorem ensures that, for any Borel $T$-invariant probability measure $\mu$ and every $\mu$-integrable observable $\varphi: Y \to \mathbb R$, the sequence of averages converges at $\mu$-almost every point in $Y$.
So, the set of irregular points is negligible with respect to any $T$-invariant probability measure.
In the last decades, though, there has been an intense study concerning the set of points for which Cesàro averages do not converge. Contrary to the previous measure-theoretical description, the set of the irregular points may be Baire generic.
We introduce a notion of sensitivity with respect to a continuous real-valued bounded map which provides a sufficient condition for a continuous transformation, acting on a Baire metric space, to exhibit a Baire generic subset of points with historic behavior.
This is a joint work with M. Carvalho (CMUP), V. Coelho (UFOB) and P. Varandas (UFBA/Univ. de Aveiro).
References:
More complete information about the seminars can be found at
https://ppge.im.ufrj.br/seminarios-de-probabilidade/
Sincerely,
Organizers: Giulio Iacobelli and Maria Eulalia Vares
PROCESSO SELETIVO: MESTRADO E DOUTORADO EM ESTATÍSTICA (IM-UFRJ)
O Programa de Pós-Graduação em Estatística do Instituto de Matemática da UFRJ (IM-UFRJ) anuncia a abertura das inscrições para o Mestrado e Doutorado.
Vagas e Oferecidas:
Mestrado em Estatística: 20 vagas
Doutorado em Estatística: 10 vagas
Bolsas de Estudo: O Programa possui um histórico de alta concessão de bolsas das agências de fomento (CNPq, CAPES e FAPERJ) para alunos em regime de dedicação exclusiva. Os valores atuais são R$ 2.100,00 (Mestrado) e R$ 3.100,00 (Doutorado), condicionados à dedicação integral ao curso.
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ATENÇÃO: RETIFICAÇÃO DO EDITAL
Foi publicada uma retificação referente ao edital n°924 (Processo Seletivo - Turma 2026_1).
Veja a retificação aqui: https://ppge.im.ufrj.br/retificacao-processo-seletivo-para-mestrado-e-doutorado-em-estatistica-2026-1/
