Information détaillée concernant le cours
Ecole d’hiver 2017
5-8 février 2017
M. Yves Tillé, UNINE (Président), Mme Caroline Gillardin, UNINE (coordinatrice)
Prof. Christian Robert, Ceremade - Université Paris-Dauphine and University of Warwick
Prof. Philip Stark, University of California, Berkeley
Prof. Rasmus Waagepetersen, Aalborg University
Professor Christian Robert
(Ceremade-Université Paris-Dauphine and University of Warwick)
Title : Approximate computational tools and statistical models
As the complexity of the statistical models keeps growing, exact computational tools for deriving complete inferential conclusions like posterior distributions in Bayesian statistics are getting harder and harder to manage. For instance, Markov chain Monte Carlo methods fail to operate in either too large dimensions of the parameters or too large size of the data. An alternative array of approximate proposals has emerged in the past decade, first as empirical substitutes to the exact solution, second as a new approach to conducting inference, producing manageable answers while acknowledging a layer of approximation. We will discuss Approximate Bayesian Computation (ABC), synthetic likelihood, expectation-propagation, and consensus Monte Carlo methods, which all pertain to this new perspective.
Professor Philip Stark
(University of California, Berkeley)
Title : Uncertainty Quantification : statistics + wishful thinking
Uncertainty Quantification (UQ) is the study of the uncertainty of inferences based on noisy data indirectly related to parameters of a model that might be defined only as code intended to approximate a complex system. Much of what is now called UQ used to be called "inverse problems." UQ research is active in applications ranging from climate to nuclear weapons, and the Bayesian/Frequentist divide is evident. I will discuss some of the underlying philosophical issues, the often-overlooked question of data quality, some common methods for UQ and their assumptions, approaches for high-dimensional and infinite-dimensional models, the use of "emulators," the prevalence of "the streetlight effect," some caveats, and open questions. Along the way, I will present a crude taxonomy of sources of error and uncertainty, sketch a generic framework for UQ, make fun of a US National Academy of Science monograph on Evaluation of Quantification of Margins and Uncertainties, trouble the unified treatment of "aleatoric" and "epistemic" uncertainty and the interpretation of probability, address the "ludic fallacy," and challenge whether all uncertainties can or should be quantified, especially as probabilities. Earthquake forecasts and climate models will be the lead applications, but I also expect to mention the US Census, solar physics, cosmology, elections, Bovine Spongiform Encephalopathy, and nuclear weapons.
Professor Rasmus Waagepetersen
(Institute of Mathematical Sciences, Aalborg University, Denmark)
Title : Statistical models and methods for spatial point processes
A spatial point process is a mathematical model for randomly distributed points in two or higher dimensional space, e.g. the locations of restaurants in a city, trees in a forest, cases of a disease in a country or galaxies in the Universe. The model may be extended to include information about covariates such as soil conditions in case of trees and random `marks such as `types of points (e.g. different types of restaurants or species of trees) or `size of associated object (e.g. the diameter of a tree at breast height).
In the lectures we will cover the following spatial point process topics:
-First and second order characteristics of spatial point processes: this includes summary statistics such as the intensity-, pair correlation and K-function.
-The Poisson process: the Poisson process is the basic model for point patterns with absence of interaction between points. It is of great interest in its own right and is furthermore the basic building block for construction of more fexible models allowing interactions between points.
-Cox and cluster point processes: in many applications, clustering between points prevents the use of a Poisson process model. In such cases Cox and cluster point process models are useful alternatives.
-Estimating functions for spatial point processes: we discuss non-parametric estimation of the K-function as well as estimation for parametric Poisson, Cox and cluster point process models.
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