Advanced Statistics

This course builds on knowledge acquired in the Statistics course at the Master in Finance.

The following topics will be critically covered both from a frequentist and from a Bayesian prospective highlighting the pros and cons of the two approaches: advanced point estimation, confidence intervals, hypothesis testing and prediction. We will also introduce Monte Carlo simulations techniques such as Markov chain Monte Carlo and Approximate Bayesian Computation. 

Additional advanced topics will be discussed such as dimensionality reduction and variable selection.

Suggested text books:

For the frequentist approach: A. Agresti and M. Kateri, “Foundations of Statistics for Data Scientists: With R and Python”.  2021, Chapman & Hall  

For the Bayesian approach: A. Agresti, M. Kateri, R. Grove, A. Mira, "Foundations of Bayesian Statistics, with R and Python" 2026, CRC Press
 

Slides will also be provided during the course.

Students are advised to bring to class their own laptop, if available.

The course aims to deepen students’ understanding of frequentist inferential statistics. The Bayesian approach to statistical inference will also be covered from both theoretical and applied perspectives. Students will learn to critically analyze a given dataset in light of specific research questions and hypotheses to be tested. The free and open-source statistical software R will be used for the more applied and data-driven components of the course but all the code introduced will also be available in python and the students can either use R or python following their own preferences.

In presenza

There will be theoretical and applied (with the R statistical software or with Python) frontal  lectures

Class participation is a mandatory component of the course grade (10% of final grade).
There will be a final exam that will comprise 90% of the final grade.

The exam will consist on a project comprising a statistical data analysis performed using the inferential tools introduced in the course. The students have to turn in the R or Python code, a PPT presentation and the final report (pdf) where the data are described together with the research questions, the analysis, the conclusions and possible further research directions. The project will be presented and discussed with possible questions ranging on the topics covered in class.