The course focuses on fundamental elements of statistical inference,
along with some principles and statistical techniques useful for the
analysis of complex data.
Knowledge and understanding: The student will be able to use
appropriate statistical models and to select among alternative models
using the relevant inferential approach.
Applied knowledge and understanding: The student will be able to use R
for analyzing (possibly big) datasets and for drawing coherent inference
on the model that could have generate the data and using it for decisions
and predictions.
Making judgements: students must show that they know how to choose
the most suitable analysis strategy also in the context of analysis of a
real data set.
Communication skills: students will be able to effectively communicate
the results of data analysis by using appropriate tools
Learning skills: students, at the end of the course, will be able to consult
autonomously scientific papers, theoretical or applied, that involve the
use of basic and advanced statistical techniques

The students should have basic knowledge of elements of probability
theory and elementary statistical methods. Some basic knowledge of
software R will be also required

1. Random variables
Review of some basic concepts of probability; the multivariate normal
distribution; central limit theory and law of large numbers; statistics and
their properties. Statistical models and inference.
Examples of statistical models; the problems of statistical inference.
Basic tools for estimation and testing statistical hypotheses.
Approaches to statistical inference and design issues (16 hours)
2. Theory of maximum likelihood estimation
The likelihood function; maximum likelihood estimation; large sample
properties; AIC and model selection; numerical aspects (12 hours)
3. Elements of Bayesian Inference (12 hours)
4. Linear and generalized linear models
The theory of linear models; regression diagnostics and model selection;
generalized linear models; prediction; cross validation (16 hours)
5. Some extensions. Multilevel extensions; nonlinear effects and
semiparametric regression (Generalized Additive Models); decision trees
(16 hours)
6. Computer labs
Application of the methods using the R software (12 hours)

- Agresti A., Katery M.: Foundations of Statistics for Data Scientists: With
R and Python, Chapman & Hall, 2021 (Main Text)
- S.N. Wood: Core Statistics, Cambridge University Press, 2016
(Supplementary text)
- Maindonald J., Braun W.J.: Data Analysis and Graphics Using R – An
Example-Based Approach (Third Edition);
Cambridge University Press, 2010 (Supplementary text)
- Efron B., Hastie T.: Computer Age Statistical Inference – Algorithms,
Evidence, and Data Science. Cambridge University Press, 2016
(Supplementary text)
Additional material and information will be available at the course web
page.

The course will be delivered by traditional lectures and practical
computer sessions.
Students will be encouraged to participate at discussion on selected
topics during the lectures.
In the practical sessions the software R will be used to illustrate some of
the main ideas and techniques by analysing some real datasets.

The course will make use of teaching tools available on the moodle2,
MS/Teams and wooclap platforms. In addition, all students are expected
to use R software, so they need to have or have access to a computer

The evaluation takes place at different times and in several ways:
- For attending students:
1. During the course, possibly, homework will be assigned to be delivered
within the established deadlines;
2. Some (2 or 3) intermediate tests will be held during the course;
3. The student must submit a report in which he/she exposes the result of
a project assigned at the end of the course.
The final evaluation will take place by averaging the marks obtained in
the 3 parts (with weights respectively equal to 0.1, 0.5, 0.4).
The three parts of the exams are such that it is possible to judge the
achievement of the training objectives as set out above.
- For non-attending students:
students will participate to an oral exam in which they will also be asked
to carry out some analyses using the R.

This course covers some topics related to one or more objectives of the
2030 Agenda for the Sustainable Development of United Nations