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 $R(3,k)\geq \frac{k^2}{4\log k}$. Nessa palestra vou apresentar uma modificação do processo triângulo livre que utilizamos para mostrar que $R(3,k)\geq \frac{k^2}{3\log k}$, 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