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Academic year 2020/2021

Course ID
Teaching staff
Stefano Favaro (Lecturer)
Amir Khorrami Chokami (Lecturer)
Degree course
Insurance and Statistics
1st year
Teaching period
First semester
Course disciplinary sector (SSD)
SECS-S/01 - statistica
Type of examination
It is very important for the students to be familiar with the basic topics in mathematics, probability and statistics acquired in the three-year undergraduate program. These topics are presented in the short course "Essentials of Mathematics and Probability" usually given in September: see for more details.

Sommario del corso


Course objectives

Ability to solve, through the use of simulation tools, some standard problems in probability and statistical inference. Ability to apply statistical concepts and statistical techniques with respect to the point estimation, hyphotesis testing and confidence sets. Ability to the code with the language R and to use some of its main packages.


Results of learning outcomes

Knowledge and understanding
Advances knowledge of statistical modeling via point estimation, hypothesis testing and confidence intervals; basic knowlegde of Monte Carlo simulation techniques for statistical models; basic knowlegde of the language R.

Applying knowledge and understanding
Ability to convert various problems of practical interest into statistical models and make inference on it; ability to implement a Monte Carlo simulation of a statistical model using the language R.

Making judgements
Students will be able to discern the different aspects of statistical modeling and of  Monte Carlo simulation with the language R.

Communication skills
Students will properly use statistical and probabilistic language arising from the classical statistics and Monte Carlo simulation; students will properly use the language R.

Learning skills
The skills acquired will give students the opportunity of improving and deepening their knowledge of the different aspects of statistical modeling and Monte Carlo simulation using the language R.


Course delivery

With regards to statistics, the course is composed of 48 hours of lectures, including lectures dedicated to excercices. For the AY 2020/2021, the course will be held remotely with lectures pre-recorded. Recorded lectures will be made available on the course's Moodle page (see link below) in due time. Additional activities to favour interactions between professors and students may be organised as online meetings. In particular, for the entire duration of the course, Stefano Favaro will be available to meet students on Webex every Tuesday from 11am to 1pm. The Webex link will be available on Moodle.

With regards to simulation, lectures are mainly devoted to the theory of Monte Carlo simulation. The course is composed of 48 hours of lectures which (for the AY 2020/2021) will be held:

  • In presence according to the official timetable; Students can also participate via webex, link on Moodle platform.
  • Remotely, with pre-recorded lectures.

In any case, the videos of the lectures will be available on Moodle, together with the teaching material and updates.


Learning assessment methods

During the Covid-19 emergency the learning assessment method consists in a written exam with video surveillance on Webex.

With regards to statistics, the exam has the durantion of 1 hour and 15 minutes and it consists of three parts

1) an exercise on the topics (probability) presented during the preliminary course taught by Cecilia Scarinzi; the maximum score for the excercise is 3/33

2) a question requiring a formal discussion of one of the main topics of statistical infence based on the likelihood function; the maximum score for this question is 18/33

3) an exercise on the topics (statistics) presented during the course; the maximum score for the excercise is 12/33


With regards to simulation, the exam has the duration of 1 hour and it consists of one/two exercises and theory questions. Points attributed to each question/exercise depend on the complexity of the exercises/questions they refer to. Exercises can require to draft an R-script. More specific instructions are uploaded on Moodle and will also be sent to students registered to the exam via their institutional email addresses.


Support activities

No extra activities.



1. Statistics: The module deals with some key themes of the theory of statistical inference, with emphasis on the role of the likelihood function. Topics include

  • Random samples and their distributions, the statistical model, the likelihood function, exponential family.
  • Sufficient statistics and minimal sufficient statistics, finite properties for estimators, asymptotic properties for estimators, methods for evaluating estimators.
  • Methods for constructing point estimators: method of moments and generalizations, method of the least square errors, method of maximum likelihood, methods of minimum distance. 
  • Hypothesis testing: probabilistic structure of hypothesis testing, Neyman-Pearson lemma, likelihood ration tests, asymptotic tests, confidence sets; nonparametric tests

2. Simulation: this module introduces various computational statistical methods. In prticular, the program includes some computationally intensive methods in statistics, such as Monte Carlo methods and the bootstrap. An important part of the module will be devoted to practicals. All the methods discussed during the course will be implemented in the R software.

Topics include:

  • Preliminaries:
    • Random variables/vectors and probability distributions;
    • Theorems for sequencies of random variables.
  • Transformations of random variables/vectors.
  • Introduction to R software.
  • Pseudo-random number generators.
  • Generating discrete and continuous random variables:
    • The Inverse-transform method;
    • The Transformation method;
    • The Composition method;
    • The Acceptance-Rejection method;
    • The Alias method;
    • The Polar Method for generating Normal random variables. 
  • Monte Carlo integration methods.
  • Variance reduction techniques:
    • Antithetic Variables;
    • Control Variates;
    • Stratified Sampling;
    • Importance Sampling;
    • Sampling Importance Resampling.
  • The Bootstrap Method and the Jackknife.
  • The Expectation-Maximization Method.

Suggested readings and bibliography


1. Probability: • Cifarelli, D.M. (1998). Introduzione al cacolo delle probabilità. McGraw-Hill; • Baldi, P. (2011). Calcolo della probabilità. McGraw-Hill; • Grimmett, G. and Welsh, D. (2014). Probability: an introduction. Oxford University Press.

2. Statistics:  • Casella, G. and Berger, R. (2001). Statistical inference. Cengage Learning Press.

3. Simulation: • Ross. S.M. (2012). Simulation, 5th Edition. Academic Press. • Jones, O., Maillardet, R. and Robinson A. (2014). Introduction to scientific programming and simulation usig R, 2nd Edition. Chapman and Hall/CRC.


Class schedule



The methods of teaching activity could change in according to the limitation imposed by the current health crisis. In any case the e-learning mode is guaranteed throughout the academic year.

Le modalità di svolgimento dell'attività didattica potranno subire variazioni in base alle limitazioni imposte dalla crisi sanitaria in corso. In ogni caso è assicurata la modalità a distanza per tutto l'anno accademico.

Last update: 22/03/2021 08:08
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