École d’hiver 2021

8 -10 février 2021 dès 8h45

Prof. Sebastian Engelke, UNIGE

Caroline Gillardin, coordinatrice CUSO

- Prof. Anthony Davison - EPFL - Title : Bootstrap Methods and their Application

- Dr. Yoav Zemel - University of Cambridge - Title : Introduction to Optimal transport in statistics

- Dr. Thordis L. Thorarinsdottir - Norwegian Computing Center - Title : Forecast evaluation

Prof. Anthony Davison (EPFL)

Title : Bootstrap Methods and their Application

Bootstrap methods are computer-intensive methods of statistical analysis that use simulation to calculate standard errors, confidence intervals and significance tests. They are widely used in applications to avoid parametric assumptions and to obtain accurate small-sample inferences. This course is a brief introduction to some key ideas, based on `Bootstrap Methods and their Application' by Davison and Hinkley (1997, Cambridge University Press). The topics to be covered are basic notions, confidence intervals, several samples, variance estimation, hypothesis tests and regression.

PDF Lectures

Dr. Yoav Zemel (University of Cambridge)

Title : Introduction to Optimal transport in statistics

Optimal transport (or Wasserstein) distances quantify the difference between probability distributions by measuring the minimal effort required to reconfigure one distribution in order to recover the other. They have become a popular tool in a wide range of applications, where objects with complex geometric structure are to be compared. This course will give a brief introduction to some of the properties of Wasserstein distances that make them a versatile tool for statisticians. Much of the course will be based on An Invitation to Statistics in Wasserstein Spaces, and the last part on the papers Optimal Transport: Fast probabilistic Approximation with Exact Solvers and Randomised Wasserstein barycenter computation: Resampling with statistical guarantees. We shall cover basic notions, the barycenter problem, alignment for point processes, and some computational aspects.

The slides can be found on this link (there may be still some changes) : https://www.dpmms.cam.ac.uk/~yz668/cuso.html

Dr. Thordis L. Thorarinsdottir (Norwegian Computing Center)

Title : Forecast evaluation

Forecast verification methods are needed to both diagnose prediction models and assess their effectiveness. These lectures will focus on verification methods for probabilistic predictions of continuous variables in one or more dimensions. In this case, it has been stated that the predictive distributions should be as sharp as possible subject to calibration. Here, calibration refers to the statistical consistency between the forecast and the observation, while sharpness refers to the concentration of the forecast uncertainty; the sharper the forecast, the higher information value will it provide, as long as it is also calibrated. We will cover approaches to empirically assess forecast calibration followed by a discussion of scoring rules to assess accuracy. Scoring rules provide a quantitative assessment of probabilistic predictions by assigning a numerical score based on the predictive distribution and on the event or value that materializes, and they should optimally fulfill certain decision-theoretic properties. In addition, we will specifically consider the case of predicting and evaluating extreme events, as well as the case when the predictive distribution should be compared to a corresponding empirical distribution of observed data rather than a single value.

The best preparation for the students would be to look at this book chapter: Link

PDF Lecture 1

PDF Lecture 2

PDF Lecture 3

Online - On Zoom

Programme

Gratuite

Questions : Caroline Gillardin ([email protected]). Tel 032 718 29 04

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