This is the home page of a Ph.D. level course offered at the National Ph.D. in AI - Society. The program covers the basic methodologies, techniques and tools of statistical analysis. This includes basic knowledge of probability theory, random variables, convergence theorems, statistical models, estimation theory, hypothesis testing, bayesian inference, causal reasoning. Other topics covered include bootstrap, expectation-maximization, and applications to machine learning problems.

The course is an extract of the M.Sc. level course Statistics for Data Science.

• Andrea Pugnana
  • Università di Pisa
  • https://andrepugni.github.io/
  • andrea [dot] pugnana [at] di [dot] unipi [dot] it

• Salvatore Ruggieri
  • Università di Pisa
  • http://pages.di.unipi.it/ruggieri/
  • salvatore [dot] ruggieri [at] unipi [dot] it

Students should be comfortable with most of the topics on mathematical calculus covered in:

• [P] J. Ward, J. Abdey. Mathematics and Statistics. University of London, 2013. Chapters 1-8 of Part 1.

You can refresh such notions through this recording and slides.

The following is the mandatory text book:

• [T] F.M. Dekking C. Kraaikamp, H.P. Lopuha, L.E. Meester. A Modern Introduction to Probability and Statistics. Springer, 2005.

Some running examples will be provided using the R programming language. However, knowledge of R is not required nor mandatory for the exam.

• R
• R Studio

Ph.D. students may do an exam (on a voluntary basis) in the form of a report and a presentation on an advanced topic/survey to be agreed upon. The topic is typically related/relevant to the objectives of the Ph.D. studies of the student.

The steps are the following:

• Identify at least three papers related to your Ph.D. research that involve some of the topics covered in the course
• Submit them to instructors who have to accept the proposed papers as relevant
• If papers are approved, students have to write a short report (8 pages minimum - 12 pages maximum) reviewing the proposed papers and send it to the instructors
• A brief oral discussion will follow (dates to be decided individually with instructors). Slides might be prepared for the discussion.

The deadline to present the report and discuss the report is December 18th 2025.

Ph.D. students will receive an attendance statement if they attend at least 7 out of the 10+1 classes.

Please, subscribe to the course Teams channel to receive updates on the course.

Lessons will be both live-streamed (see Teams channel) and in presence at the Department of Computer Science, University of Pisa.

Teaching material might be updated after the classes to align with actual content and to correct typos. Be sure to download the updated versions.