Title: "A Central Limit Theorem for intransitive dice"

Speaker: Daniel Ungaretti

Abstract: Consider dice that are allowed to have different numbers of faces and any number on each face. Die A is said to be better than die B, denoted A ▷ B, if it has a larger probability of winning. This ordering of dice is not transitive: it is possible that A ▷ B ▷ C ▷ A. In this talk we present results on the probability of random dice (with i.i.d. faces) forming an intransitive chain, as the number of faces of each die goes to infinity. We prove a Central Limit Theorem for such dice, combining the method of moments with simple graph theory arguments.

March 25, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time).

Local: room C116 - Bloco C - CT – Instituto de Matemática – UFRJ.

More complete information about the seminars can be found HERE.

Sincerely,
Organizers: Giulio Iacobelli and Maria Eulalia Vares

Probability Seminar “Inhomogeneous percolation with random one-dimensional reinforcements”

January 15, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)

Local: room C116 - Bloco C - CT – Instituto de Matemática – UFRJ. There will be no transmission online.

Speaker: Alan Bruno do Nascimento (UFMG)

Abstract: In this talk we consider inhomogeneous Bernoulli bond percolation on the graph GxZ, where G is an infinite connected graph with bounded degree and Z is the set of integers. In 1994, Madras, Schinazi and Schonman showed that there is no percolation in Z^d  if the edges  are open with a probability of q<1 if they lie on a fixed axis and with a probability of p<p_c(Z^d) otherwise. Here, we consider a region given by boxes with iid radii centered along the vertical axis 0xZ of GxZ. We allow each edge to be open with a probability of q<1 if it is inside this region and with a probability of p<p_c(GxZ) otherwise. The goal of the talk is to show that, even if the region is connected, occurrence or not of percolation in this inhomogeneous model depends on how sparse and how large are the boxes placed along the axis. We aim to give sufficient conditions on the moments of the radii as a function of the growth of the graph G for percolation not to occur.
This is a joint work with Rémy Sanchis and Daniel Ungaretti.

More complete information about the seminars can be found at DME

Organizers: Giulio Iacobelli e Maria Eulalia Vares

Probability Seminar “New results for the simple parking process”

March 11, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)

Local: Sala C116, Instituto de Matematica - UFRJ

Speaker: Sandro Gallo (DEs -UFSCar)

Abstract: We consider the parking process on the grid with a simple occupancy scheme, which is defined as follows. Initially, all the sites in Λn := {−n, . . . , n} d are empty. At each step, a site is chosen uniformly at random in Λn and if it and its nearest neighbors are empty, the chosen site is occupied. Once occupied, the site remains so forever. We will discuss the statistical properties of the proportion of occupied sites for this model and for its thermodynamic limit defined on the integer grid Z d . This talk is based on ongoing work in collaboration with Alejandro Roldan (UdeA, Colombia), ´ Alexander Leon (UdeA, Colombia) and Cristian Coletti (UFABC, Brazil)

More complete information about the seminars can be found at DME

Probability Seminar ''Causal Inference Under Mis-Specification: Adjustment Based on the Propensity Score''

December 11, from 3:30 p.m. to 4:30 p.m. (Rio de Janeiro local time)

Local: room C116 - Bloco C - CT – Instituto de Matemática – UFRJ

Speaker:  Widemberg da Silva Nobre (IM-UFRJ)

Abstract: We study Bayesian approaches to causal inference via propensity score regression. Much of Bayesian methodology relies on parametric and distributional assumptions, with presumed correct specification, whereas the extant propensity score methods in Bayesian literature have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional ‘likelihood times prior’ posterior inference. We emphasize that causal inference is typically carried out in settings of mis-specification, and develop strategies for fully Bayesian inference that reflect this. We focus on methods based on decision-theoretic arguments, and show how inference based on loss-minimization can give valid and fully Bayesian inference. We propose a computational approach to inference based on the Bayesian bootstrap which has good Bayesian and frequentist properties.

Link of the paper HERE.

More complete information about the seminars can be found at DME.

Sincerely,

Organizers: Giulio Iacobelli e Maria Eulalia Vares