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. 

Survival analysis and Longitudinal data analysis will also be covered.

Suggested text books:

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

For the Bayesian approach: Bayesian Data Analysis, Gelman, A. and Carlin, J. B. and Stern, K. S. and Dunson, D. B. and Vehtari, A. and Rubin, D. B., 2014
 

For longitudinal data analysis: Analysis of Longitudinal. Data,Diggle, P. J., Heagerty, P., Liang, K., and Zeger, S. L. 2002
University Press.

For survival analysis: Survival analysis, Techniques for Censored and Truncated Data. Klein, J. P. and Moeschberger, M. L.,2003

For the applied part of the course students are referred to the online material available here https://www.r-project.org

Lecture notes will also be provided during the course.

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

The course aims to deepen notions of frequentist inferencial statistics and to introduce new topics such as survival analysis and longitudinal data analysis. The Bayesian approach to statistical inference will also be covered from a theoretical and applied point of view. The students will be able to critically analyze a given data set having in mind research questions and hypothesis to be tested. The freeware statistical software R Project will be used for the more applied and data driven part of the course. 

In presence

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

Class participation is a mandatory component of the course grade.
There will be a final exam that will comprise 100% 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.

• Attend classes and work on the HMW assignements, 27.04.24 - 27.04.24 (Optional)