This is a short course of the Mathematics for daTa scieNce study plan

Elena Stanghellini

Elena Stanghellini,
(University of Perugia)
Bio Elena Stanghellini is Professor of Statistics at the University of Perugia. After completing her Ph.D. in 1995 at the University of Florence, she was Research Fellow at the Open University, to then join the University of Perugia in 1997. In 1999 she was Jemolo Fellow at the University of Oxford. Currently she is Affiliated Professor at the Umeå University. Her research focuses on Graphical Markov Models, both from the theoretical and applied view point. She has been working on identification of Graphical Markov Models with unobserved nodes, causal inference and bias induced by informative selection or drop-out. In 2020, she was Member of the Advisory Board of ISTAT for the design and implementation of sample surveys to measure and monitor epidemiological parameters of COVID-19 pandemic.

Abstract

The course aims to provide the basic concepts of causal inference and mediation analysis within a graphical model framework. The notion of causal graphs will be introduced and the assumptions to identify the Total Causal Effect will be discussed. We then introduce the decomposition of the Total Causal Effect into natural direct and indirect causal effects, when one mediator is present, along with the necessary identifying assumptions. Possible alternatives to this kind of effects will also be presented. Extension to more mediators is discussed. Links with sensitivity analysis will also be illustrated.

Lecture 1: Causal Inference and DAGs

  • Three approaches to causal inference
  • Total causal effect (TCE)
  • Causal DAGs
  • Nonparametric identification of TCE

Lecture 2: Decomposition of TCE into direct and indirect effects

  • Mediation analysis with one mediator: definitions
  • Nonparametric mediation
  • Parametric mediation via LSEM
  • Parametric mediation for more complex systems

Lecture 3: Sensitivity against unobserved confounders

  • The notion of sensitivity
  • Some old and recent results on sensitivity

Schedule

  • Wednesday, 3 December 2025, 8:30-10:30, room A223 @ Povo1
  • Thursday, 4 December 2025, 8:30-10:30, room A219 @ Povo1
  • Friday, 5 December 2025, 8:30-10:30, room A215 @ Povo1

Details