Assessing the Distribution Consistency of Sequential Data

Given n observations, we study the consistency of a batch of k new observations, in terms of their distribution function. We propose a non-parametric, non-likelihood test based on Edgeworth expansion of the distribution function. The keypoint is to approximate the distribution of the n+k observations by the distribution of n-k among the n observations. Edgeworth expansion gives the correcting term and the rate of convergence. We also study the discrete distribution case, for which Cram\`er's condition of smoothness is not satisfied. The rate of convergence for the various cases are compared.Comment: 20 pages, 0 figure

La précognition est-elle démontrée ?

International audienceEn général, quand quelqu'un dit avoir la preuve que les " dons psychiques " existent, telles la télépathie ou la prémonition, la réaction du monde académique se résume à un haussement d'épaule. Quand réaction il y a, évidemment. Le débat actuel a été lancé par Daryl J. Bem, professeur émérite [1] de psychologie à Cornell University dans The Journal of Personality and Social Psychology (une revue tout à fait respectable). Il décrit les expériences qu'il a faites afin, dit-il, d'amener ses collègues à au moins considérer la possibilité de l'existence de tels pouvoirs. Du coup, les uns crient au scandale dans le New York Times. D'autres à la mauvaise utilisation généralisée des statistiques en sciences sociales. Et d'autres encore subodorent un canular

Spatio-temporal Functional Regression on Paleo-ecological Data

The influence of climate on biodiversity is an important ecological question. Various theories try to link climate change to allelic richness and therefore to predict the impact of global warming on genetic diversity. We model the relationship between genetic diversity in the European beech forests and curves of temperature and precipitation reconstructed from pollen databases. Our model links the genetic measure to the climate curves through a linear functional regression. The interaction in climate variables is assumed to be bilinear. Since the data are georeferenced, our methodology accounts for the spatial dependence among the observations. The practical issues of these extensions are discussed

Non-Adaptive Policies for 20 Questions Target Localization

The problem of target localization with noise is addressed. The target is a sample from a continuous random variable with known distribution and the goal is to locate it with minimum mean squared error distortion. The localization scheme or policy proceeds by queries, or questions, weather or not the target belongs to some subset as it is addressed in the 20-question framework. These subsets are not constrained to be intervals and the answers to the queries are noisy. While this situation is well studied for adaptive querying, this paper is focused on the non adaptive querying policies based on dyadic questions. The asymptotic minimum achievable distortion under such policies is derived. Furthermore, a policy named the Aurelian1 is exhibited which achieves asymptotically this distortion

Spatial cluster detection using the number of connected components of a graph

The aim of this work is to detect spatial clusters. We link Erdös graph and Poisson point process. We give the probability distribution function (pdf) of the number of connected component for an Erdös graph and obtain the pdf of the number of cluster for a Poisson process. Using this result, we directly obtain a test for complete spatial randomness and also obtain the clusters that violates the CSR hypothesis. Border effects are computed. We illustrate our results on a tropical forest example

Supplementary Material for: Homogeneity and identity tests for unidimensional Poisson processes with an application to neurophysiological peri-stimulus time histograms–R version

R version of the Supplementary material for "Homogeneity and identity tests for unidimensional Poisson processes with an application to neurophysiological peri-stimulus time histograms.