28436 - Probability and Statistics

Academic Year 2025/2026

Course contents

Introduction to computational statistics and R programming.

Random Variable Generation. Uniform simulation, the inverse transform, general transformation methods, discrete distributions.

Monte Carlo Integration. Introduction, classical Monte Carlo integration. Importance sampling.

Monte Carlo Optimization. Introduction, numerical optimization methods, stochastic search (basic solutions, stochastic gradient methods, simulated annealing).

[Tentative] Bootstrapping. Introduction, parametric and nonparametric bootstrap. 

Readings/Bibliography

  • Robert, C. & Casella, G. (2010). Introducing Monte Carlo Methods with R. New York: Springer-Verlag.

  • Efron, B. & Tibshirani, R. J. (1993). An introduction to the bootstrap. London: Chapman & Hall/CRC.

Teaching methods

• Conventional lectures

Assessment methods

The exame is comprised of a set of open questions and/or practical exercises to be solved using the software R.

The final mark of the "Numerical Analysis" course is defined as the arithmetic mean of the marks obtained in the test for the Numerical Analysis module and a written exam for the Computational Statistics module.

 

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students ) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

Teaching tools

Additional material provided by the teacher (iol.unibo.it)

Office hours

See the website of Saverio Ranciati