Ateneo - UPO

Introduction to computational statistics with particular attention to models and algorithms to generate random variables, multivariate data visualization, statistic inference, Monte Carlo methods, resampling. Introduced methodologies will be implemented by means of the statistical software R.

- M. L. Rizzo (2019): Statistical Computing with R, Second Edition. Chapman & Hall, Boca Raton.

- Lecture notes.

The goals of the course are (Dublin descriptors)
• knowledge and understanding: know the introduced statistical techniques
• applying knowledge and understanding: know how to implement and interpret them in real and simulated scenarios
• making judgements: be able to make autonomously judgements on the use of the introduced methodologies
• communication skills: know how to communicate the results, advantages and limitations of the methodologies implemented even to non-experts
• learning skills: know how to extend the concepts and ideas seen in the course to new settings.

Fundamentals of mathematics, probability and statistics.

Both theoretical and practical classes will be held in a computer lab. Frequency of lessons is highly recommended.

Further informations (such as link to software website) can be found at the web page of the course: https://dir.uniupo.it/

Students with physical disabilities, Learning Disabilities or Special Education Needs can request
specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse

e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/services-
students-physical-or-learning-disabilities

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents-physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The exam is formed by an oral examination that consists in theoretical questions and in a discussion about a possibly essay.

0. Introduction to R.
1. Data manipulation in R. Visualization of data (elements of descriptive Statistics).
2. Generating data.
3. Inferential statistics (point estimation, Hypothesis test, (non-)parametric methods)
4. Introduction to stochastic processes (Discrete and continuous time Markov Chains)
5. Introduction to Bayesian statistics and simple Monte Carlo Markov Chain (MCMC) techniques
6. Resampling tecniques (bootstrap and jackknife)

The topics of the course may undergo changes according to the didactic needs that emerge during the course.

At the end of the classes, students should (Dublin descriptors) • Knowledge: know the main reasons and applications that require the introduction of methods for generating random numbers, for Monte Carlo simulations and for resampling. • Skills and abilities: knowing how to evaluate the areas of application, implement and interpret, in simulated and real scenarios, the methodologies tackle in classes. Knowing how to communicate, even to non-experts, the results, advantages and limitations of the methodologies implemented. Knowing how to extend the concepts and ideas seen in the course to new contexts.