C8296 - STATISTICA PER L'ANALISI DEI DATI

Learning outcomes

The course aims to provide students with knowledge of methods for database management and data analysis through the use of statistical software. It covers methods for data visualisation, data description and inference from sample data. In the second part, the course aims to provide students with an understanding of advanced inference methods based on the likelihood approach and its numerical maximisation. By the end of the course, students will be able to select and apply the most appropriate statistical methodologies for data analysis effectively and consistently in research and applied studies.

Course contents

Part I. Methods for database management and data analysis

• Introduction to the R statistical environment.
• Procedures for importing, managing and transforming databases in R. Guided illustrative examples.
• Commands for carrying out exploratory analyses using statistical measures and graphical representations in R. Guided illustrative examples.
• R functions for studying discrete and continuous probability distributions and generating random numbers from a specified probability distribution. Guided illustrative examples.
• Methods and practical tools for comparing an empirical distribution with a theoretical distribution. The normal-quantile plot and the quantile-quantile plot. Guided illustrative examples.
• Techniques for characterising and simulating sample distributions. Guided illustrative examples.
• R commands and functions for point and interval estimation. Guided illustrative examples.
• R functions for performing significance tests. Guided illustrative examples.

Part II. Advanced inference methods based on the likelihood approach

• Statistical models. Identifiability of a statistical model. Unidentifiable models. Illustrative examples.
• The likelihood function. The principle of likelihood. Illustrative examples.
• Statistics, sufficient statistics and minimal sufficient statistics. Illustrative examples and guided exercises.
• Exponential families. Examples and guided illustrative exercises.
• The maximum likelihood estimation method. Examples and guided illustrative exercises.
• Techniques for the numerical maximisation of the likelihood function. Guided illustrative examples.
• Observed information and Fisher’s expected information. Examples and guided illustrative exercises.
• Properties of maximum likelihood estimators. Examples and guided illustrative exercises.
• The problem of hypothesis testing and its solution according to the Neyman-Pearson approach. Likelihood ratio tests for simple and composite systems of hypotheses and their main applications.

Readings/Bibliography

Essential materials for exam preparation

• A. Agresti, M. Kateri, Fondamenti di statistica per data scientists. Con R e Python. EGEA, Milano, 2022, chapters 1-5 and appendices A, C. Unibo students can access an electronic version of the book via this link. To this goal, they have to log in from workstations connected to the University network or remotely via the EZproxy service.
• S. Iacus, G. Masarotto, Laboratorio di statistica con R. 2° edizione, McGraw-Hill, Milano, 2007
• H. Wickham, M. Cetinkaya-Rundel, G. Grolemund. R for Data Science: Import, Tidy, Transform, Visualize, and Model Data (2e). O’Reilly. an electronic version of the book is accessible via this link.
• A. Azzalini, Inferenza statistica. Una presentazione basata sul concetto di verosimiglianza. 2° edizione, Springer-Verlag Italia, Milano, 2001, capitoli 1-4
• Handouts prepared by the lecturer containing teaching materials to support students’ studies and summaries of the topics covered during the lectures.

Teaching methods

Weekly lessons
Lessons will take place in a computer lab. In the first part of the course, the activities led by the lecturer are predominantly practical in nature. For the topics listed for this part in the ‘Contents’ section, lessons will include a brief review (or introduction) of indicators and methods for data analysis, followed by their practical application using R commands and functions. In the second part of the course, for each of the advanced inference methods based on the likelihood approach listed in the ‘Contents’ section, basic theoretical explanations are provided, followed by illustrative examples in R and guided exercises.

Self-study
Between lectures, students are advised to gradually consolidate their knowledge by revising the lecture materials, reviewing the statistical analyses carried out during the lectures, completing any reading and practical activities suggested by the lecturer, and reflecting on the reasoning demonstrated in the laboratory to interpret and communicate the results of the analyses. Students are also encouraged to regularly consult the ‘Virtual Learning Environment’ platform (https://virtuale.unibo.it/) to prepare for practical activities, consolidate key concepts and practise the type of reasoning and communication required for assessment.

Further information on teaching methods

• Attending lectures and actively participating in all teaching activities is the first and simplest way to begin learning. For this reason, although attendance at lectures is not compulsory, it is strongly recommended.
• To ensure students are up to speed on certain topics covered in the first part of the course, it is recommended that they attend the lectures for C8399 - REFRESH COURSE DI PROBABILITA' E STATISTICA (20 hours scheduled during the week from 7 September 2026 to 11 September 2026; 4 additional credits on top of the minimum 120 credits required to obtain the Master’s degree).
• Given the nature of the course and the teaching methods used, attendance at this course requires all students to have previously completed Modules 1 and 2 of the e-learning course on safety in study environments.
  

Assessment methods

The aim of the examination is to assess the level of knowledge and skills set out in the ‘Contents’ section. In particular, the examination aims to assess the level of proficiency achieved in the use of the tools available in the R statistical environment and in the advanced inference methods covered during the lectures.

To this end, the assessment consists of an examination organised into a practical component and a written component. The practical component takes place in a computer lab, lasts one hour and involves solving exercises using R commands. The written component takes place in a lecture hall, lasts one hour and consists of open-ended questions (grouped in the form of exercises) concerning the methods covered during the lectures and their applications. To answer some of the questions in the written examination, it may be necessary to carry out calculations, which may be performed using a calculator.

During both components of the examination, candidates are not permitted to consult notes or books; the use of any type of electronic device (e.g. earphones, smartphones, smart glasses, smartwatches, etc.) is not permitted. The use of a calculator is permitted for carrying out calculations during the written examination.

For each exercise in each of the two components, the corresponding maximum mark used to determine the final mark is indicated. The sum of the maximum marks awarded for the exercises in each of the two examinations is 16. The overall assessment of a student’s performance, expressed out of 30, is calculated by adding together the marks awarded for the individual exercises completed by the student. Overall marks of 31 and 32, determined in this way, correspond to a final mark of 30 with distinction. The examination is considered passed if the mark achieved is at least 18.

The maximum mark for each exercise is determined by taking into account the length and complexity of the reasoning required to produce the correct answer; it may therefore vary between exercises within the same exam. The mark awarded for the exercises completed by the student is determined by simultaneously taking into account the completeness, appropriateness and consistency of the solution in relation to the requirements set out in the questions comprising each exercise.

The examination and the marking scheme are the same for all students (both those attending and those not attending lectures). Whether or not a student has attended lectures is not taken into account in the assessment of their knowledge during the examination.

The use of AI is prohibited in the assessment of learning for this course. Any use constitutes a breach of academic integrity.

Further useful information regarding the exam

• In accordance with the degree programme regulations, four exam sessions are scheduled for each academic year: the first in January, the second in February, the third in June and the fourth in September. The specific dates of the exam sessions are announced at the start of the academic year and can be found on the Almaesami platform.
• To sit the exam, students must be registered on the official lists available on Almaesami.
• To sit the exam, students must provide proof of your identity by presenting a valid, appropriate identity document.
• Students are permitted to withdraw from either of the two components of the examination.
• As provided for in Article 13, paragraph 1, of the University Regulations on Student Fees (http://www.normateneo.unibo.it/regolamento-di-ateneo-sulle-contribuzioni-studentesche-1), students with outstanding debts of any kind (by way of example only: student fees, late payment penalties, repayment of international mobility grants, etc.), with the University and/or the Regional Agency for the Right to Higher Education (ER.GO) may not undertake any academic procedures, including sitting examinations.
• Students are permitted to decline a passing mark on at least one occasion and no more than twice.
• It is not possible to sit an exam outside the official exam dates published on Almaesami.

Splitting the examination into two separate sittings

At the end of the first 30 hours of lectures, all students who wish to do so (whether attending or not, and whether enrolled in the first year or subsequent years) are permitted to sit the practical component of the examination (on the topics covered in the first 30 hours of lectures). Those who achieve a mark of at least 9/16 will be eligible to sit the written component of the examination during the first examination session.

Teaching tools

The handouts prepared by the lecturer for the study of the syllabus topics and exam preparation will be made available to students on the “Virtual Learning Environment” platform (https://virtuale.unibo.it/) on a weekly basis. Access is restricted to students enrolled at the University of Bologna and is granted using the login details provided upon enrolment.

These handouts and the explanations provided in class must be appropriately supplemented by the material in the reference texts and are in no way a substitute for them.

Students with disabilities who are entitled to and require adjustments to their learning and/or assessment are invited to inform the lecturer promptly so that the most appropriate study and/or examination arrangements for their specific situation can be identified.

Office hours

See the website of Gabriele Soffritti