Statistical inference

Maria Pia Victoria Feser, Cinzia Viroli

  • Date:

    02 DECEMBER 2024
    -
    28 FEBRUARY 2025
     from 10:00 to 16:00
  • Event location: Aula IV, Department of Statistical Sciences, Via Belle Arti 41 (STAT PhD Classes Virtual Room on need) - In presence and online event

  • Type: Cycle 40 - Mandatory Courses

Aims: to explore a number of statistical principles. The way through is to address the nature of diverse statistical approaches, as for example Bayesian or Frequentist, but not only. To do so, we base the learning approach on the general idea of inference as a statistical decision problem, which is linked directly or indirectly to statistical modelling. We encourage students to tackle the challenges that include the analysis of large data sets, complex dependent data, dimension reduction, diverse types of outcomes, the potential presence of outliers, etc. We also deal with model selection, accurate prediction, model interpretation; all of these challenges need for alternative extensions to the classical asymptotic likelihood theory.

Learning outcomes: An appreciation for the complexity of classical statistical inference, recognition of its inherent potential drawbacks as well as the role of expert judgement, the ability to criticise familiar inference methods, knowledge of the potential adaptations that need to be made in order to address apparently simple but in fact difficult scientific questions.

Course contents
Module 1. Foundations of Statistics (Prof. C. Viroli)

  • Preliminaries on asymptotic tools.
  • Inference Paradigms.
  • Asymptotic Theory of Likelihood.
  • Bayesian Inference.
  • Extensions of Likelihood-based Inference.
  • Practical Applications in R.
  • Advanced Statistical Functionals.


Module 2. Beyond conventional statistical inference (Prof. M. Feser)

  • High dimensional inference
  • Robust inferential methods
  • Large scale hypothesis testing
  • Sparse modelling