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Título: On the threshold of spread-out contact process percolation
Palestrante: Daniel Valesin (University of Groningen)

Data: 27 de julho de 2020 (segunda-feira)
Hora: 15:00 h

O seminário será realizado no GoogleMeet. Clique AQUI para acessar. 

Abstract: We study the stationary distribution of the (spread-out) d-dimensional contact process from the point of view of site percolation. In this process, vertices of \Z^d can be healthy (state 0) or infected (state 1). With rate one infected individuals recover, and with rate \lambda they transmit the infection to some other vertex chosen uniformly within a ball of radius R. The classical phase transition result for this process states that there is a critical value \lambda_c(R) such that the process has a non-trivial stationary distribution if and only if \lambda > \lambda_c(R). In configurations sampled from this stationary distribution, we study nearest-neighbor site percolation of the set of infected sites; the associated percolation threshold is denoted \lambda_p(R). We prove that \lambda_p(R) converges to 1/(1-p_c) as R tends to infinity, where p_c is the threshold for Bernoulli site percolation on \Z^d. As a consequence, we prove that \lambda_p(R) > \lambda_c(R) for large enough R, answering an open question of [Liggett, Steif, AIHP, 2006] in the spread-out case. Joint work with Balázs Ráth.

Organizadores: Guilherme Ost e Maria Eulalia Vares


Título: Quantification under prior probability shift: the ratio estimator and its extensions
Palestrante: Rafael Izbicki (UFSCar)

Data: 13 de julho de 2020 (segunda-feira)
Hora: 15:00 h

O seminário será realizado no GoogleMeet. Clique AQUI para acessar. 

Abstract: The quantification problem consists of determining the prevalence of a given label in a target population using labels from a sample from the training population. A common assumption in this situation is that of prior probability shift, that is, once the labels are known, the distribution of the features is the same in the training and target populations. In this paper, we derive a new lower bound for the risk of the quantification problem under the prior shift assumption. Complementing this lower bound, we present a new approximately minimax class of estimators, ratio estimators, which generalize several previous proposals in the literature. Using a weaker version of the prior shift assumption, which can be tested, we show that ratio estimators can be used to build confidence intervals for the quantification problem. We also extend the ratio estimator so that it can:(i) incorporate labels from the target population, when they are available and (ii) estimate how the prevalence of positive labels varies according to a function of certain covariates.

Organizadores: Guilherme Ost e Maria Eulalia Vares


Palestra: Probabilistic model for integer partitions
Palestrante: Stella Brassesco (Instituto Venezolano de Investigaciones Científicas)

Data: 9 de março de 2020 (segunda-feira)
Hora: 15:30 h

Resumo: A family of independent random variables can be associated to the sequence p(n), which counts the number of partitions of a natural number n. The sum of those variables, suitably normalized, can be seen to converge to a Gaussian random variable, which suggests a method to obtain detailed asymptotics for p(n) an n goes to infinity. Moreover, the representation is useful to deduce asymptotic properties when the uniform distribution is considered on the set of partitions of n.

The problem is related with questions arising in several contexts.

Título: Brownian motion in inverse-square Poisson potential
Palestrante: Renato Soares dos Santos (UFMG)

Data: 29 de junho de 2020 (segunda-feira)
Hora: 15:00 h

Devido ao surto de coronavírus, o seminário habitual do Grupo de Probabilidades será realizado on-line durante os próximos meses, por meio da ferramenta gratuita de seminários on-line GoogleMeet. Os seminários acontecem às segundas-feiras a partir das 15h. às 16h (horário local do Rio de Janeiro), inicialmente a cada duas semanas (possivelmente evoluindo para um seminário semanal).

Resumo: We consider the parabolic Anderson model in d-dimensional space, i.e., the stochastic heat equation with multiplicative potential, with a random attractive potential having inverse-square singularities on the points of a standard Poisson point process. We study existence and large-time asymptotics of positive solutions via Feynman-Kac representation.

Organizadores: Guilherme Ost e Maria Eulalia Vares

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Título: Dependent Mixtures: Modelling cell lineages
Palestrante: Carlos Tadeu Pagani Zanini (UFRJ)

Data: 25/11/2019 (segunda-feira)
Hora: 15:30
Local: B106-b – Bloco B - CT – IM/UFRJ

Palestrante: Carlos Tadeu Pagani Zanini (UFRJ)

Resumo: Cell lineage data comes from single-cell transcriptomics and it is used to recover the evolutionary path of cells in a given environment. The different evolutionary stages of the cells can be probabilistically described by distinct components in a mixture model. This work proposes a Bayesian dependent mixture model where the dependence on the components of the mixture explicitly incorporates the biological structure that characterizes cell lineage applications. We use a random tree structure (Minimum Spanning Tree) not only to explain the snapshot in the latent space of the continuous development of cells from its initial stage into mature differentiated cells, but also to model the dependence structure between the clusters of cells. Regularization is incorporated in the form of a prior penalization on trees with too many nodes or with redundant edges. Consequently, the model assumes the partition of cells to depend on the lineage structure, which is more biologically reasonable then the usual multistep approach in which partitions are estimated disregarding the underlying tree structure that characterizes cell lineage data. We are able to provide full inference (with uncertainty captured by the posterior samples obtained through MCMC) on the clusters of cells (including number of clusters), on the underlying tree structure and also on pseudotimes.

Authors: Zanini, C. T. P, Paulon, G., Mueller, P.