Department of Mathematics and Statistics

Advanced courses

Advances courses in 2024-2025

Advances courses in 2023-2024

Ingrid Van Keilegom (TSE Visitor) will give a short course on duration analysis with a review of the basics and some more specialized topics on the following dates:

  • Class 1: Monday May 13 from 10 to 12 in T225
  • Class 2: Tuesday May 14 from 1:30 to 3:30 in T225
  • Class 3: Wednesday May 15 from 10 to 12:30 in T225

Title: Duration analysis: review of the basics and some more specialized topics

In this course we will start by reviewing the basics of duration analysis (censoring, Kaplan-Meier estimator, Cox model, log-rank test,…) (class 1). Then, more specialized topics will be treated, namely the topic of cure models (class 2) and of dependent censoring (class 3). Cure models are used when the event of interest (e.g. finding a new job) never happens for a proportion of the population, leading to a survival function with a mass at infinity. It is then often of interest to model and estimate separately that mass at infinity and the survival function of those with finite event times, depending on a set of covariates. Dependent censoring means that the duration time and the censoring time are not stochastically independent, whereas usually in duration analysis it is assumed that they are independent. The survival function can in that case not be identified without additional assumptions. Several models will be discussed that lead to (partially) identified survival functions. It will also be seen how the presence of covariates can help to identify the survival function.

Professor Rik Lopuhaä (TSE Visitor) gave a course on February 2024.

Title: Robust estimation of multivariate location and scatter

Abstract: in this course, we will discuss several popular methods for robust estimation of multivariate location and scatter including S-estimators and the minimum covariance determinant estimator. We will introduce these methods, explain their relationship with M-estimators, and discuss their robustness and asymptotic properties. We will also discuss the mathematical techniques that can be used to rigorously derive the properties and features of these methods, and illustrate their implementation in R and how to use them in practice.

Advances courses in 2022-2023

Peter Takac (University of Rostock, Germany) gave a course at TSE on February 2023 "Semi-linear and quasi-linear Black-Scholes-type equations in Mathematical Finance: Analytical and numerical methods with some monotonicity"

-> Syllabus (PDF)

Pierre Alquier (Riken AIP) gave courses at TSE on November 2022 "PAC-Bayes and Information bounds, with Applications to Variational Inference"

-> Syllabus (PDF)