Search results for "Uncertainty"
showing 10 items of 1010 documents
Large systems of path-repellent Brownian motions in a trap at positive temperature
2006
We study a model of $ N $ mutually repellent Brownian motions under confinement to stay in some bounded region of space. Our model is defined in terms of a transformed path measure under a trap Hamiltonian, which prevents the motions from escaping to infinity, and a pair-interaction Hamiltonian, which imposes a repellency of the $N$ paths. In fact, this interaction is an $N$-dependent regularisation of the Brownian intersection local times, an object which is of independent interest in the theory of stochastic processes. The time horizon (interpreted as the inverse temperature) is kept fixed. We analyse the model for diverging number of Brownian motions in terms of a large deviation princip…
Estimating the causal effect of timing on the reach of social media posts
2022
AbstractModern companies regularly use social media to communicate with their customers. In addition to the content, the reach of a social media post may depend on the season, the day of the week, and the time of the day. We consider optimizing the timing of Facebook posts by a large Finnish consumers’ cooperative using historical data on previous posts and their reach. The content and the timing of the posts reflect the marketing strategy of the cooperative. These choices affect the reach of a post via a dynamic process where the reactions of users make the post more visible to others. We describe the causal relations of the social media publishing in the form of a directed acyclic graph, …
S36.4: Control of false discovery rate in adaptive designs
2004
Rare events and scaling properties in field-induced anomalous dynamics
2012
We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the L\'evy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long sp…
Rough linear PDE's with discontinuous coefficients - existence of solutions via regularization by fractional Brownian motion
2020
We consider two related linear PDE's perturbed by a fractional Brownian motion. We allow the drift to be discontinuous, in which case the corresponding deterministic equation is ill-posed. However, the noise will be shown to have a regularizing effect on the equations in the sense that we can prove existence of solutions for almost all paths of the fractional Brownian motion.
Assessing uncertainty of voter transitions estimated from aggregated data. Application to the 2017 French presidential election
2020
[EN] Inferring electoral individual behaviour from aggregated data is a very active research area, with ramifications in sociology and political science. A new approach based on linear programming is proposed to estimate voter transitions among parties (or candidates) between two elections. Compared to other linear and quadratic programming models previously published, our approach presents two important innovations. Firstly, it explicitly deals with new entries and exits in the election census without assuming unrealistic hypotheses, enabling a reasonable estimation of vote behaviour of young electors voting for the first time. Secondly, by exploiting the information contained in the model…
Explicit, identical maximum likelihood estimates for some cyclic Gaussian and cyclic Ising models
2017
Cyclic models are a subclass of graphical Markov models with simple, undirected probability graphs that are chordless cycles. In general, all currently known distributions require iterative procedures to obtain maximum likelihood estimates in such cyclic models. For exponential families, the relevant conditional independence constraint for a variable pair is given all remaining variables, and it is captured by vanishing canonical parameters involving this pair. For Gaussian models, the canonical parameter is a concentration, that is, an off-diagonal element in the inverse covariance matrix, while for Ising models, it is a conditional log-linear, two-factor interaction. We give conditions un…
Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality
2017
We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.
A Galton–Watson process with a threshold
2016
Abstract In this paper we study a special class of size dependent branching processes. We assume that for some positive integer K as long as the population size does not exceed level K, the process evolves as a discrete-time supercritical branching process, and when the population size exceeds level K, it evolves as a subcritical or critical branching process. It is shown that this process does die out in finite time T. The question of when the mean value E(T) is finite or infinite is also addressed.