L'insegnamento prevede 3.0 CFU erogati con Didattica Innovativa come segue:

Blended Learning & Flipped Classroom

Corso di Studi

Codice Piano di Studio preventivamente approvato

Da (compreso)

A (escluso)

Insegnamento

Ing Ind - Inf (Mag.)(ord. 270) - MI (487) MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA

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A

ZZZZ

055703 - NONPARAMETRIC STATISTICS

055702 - NONPARAMETRIC STATISTICS

Obiettivi dell'insegnamento

Nonparametric Statistics is a course that aims at providing students with statistical and algorithmic tools for the analysis of complex data, i.e., data for which the identification of standard and classical probabilistic models is hard or not possible, through a nonparametric approach. The course is organized in theoretical classes and lab sessions and a data analysis team project. Knowledge in probability, statistical inference and multivariate statistics is required.

Risultati di apprendimento attesi

Lectures and exercises sessions will allow students to acquire the following competences:

Knowledge and understanding.

Having successfully taken the course examination, the students are expected to

- know the principles of nonparametric descriptives, inference, prediction and forecasting;

- know the correct terminology of nonparametric statistics and to be able to correctly argument the theory.

The students’ knowledge and comprehension is expected not be limited to the enunciation of definitions and results and to the solution of standard exercises, but rather to be critical and enabling to distinguish among different situations and to take appropriate choices, justifying the followed procedures.

Ability of applying knowledge and understanding.

Having successfully taken the course examination, the students are expected to

- be able to apply the attained knowledge to specific problems of data analysis;

- be able to select the principles which are useful to obtain the solutions to the problems at hand;

- be able to elicit relevant indicators and summaries from large amounts of data.

Argomenti trattati

Part I (Non parametric Multivariate Exploration)

Depth measures

Part II (Non parametric Inference)

Rank Tests

Permutational Inference (Tests and Confidence Intervals)

Booststrap Inference (Tests and Confidence Intervals)

Module: Categorical Data

Part III (Non parametric Regression)

Nonparametric Regression:Kernel methods (univariate and Multivariate); Spline Regression

Module: Nonparametric estimation in Survival Analysis: Kaplan-Meier and Nelson-Aalen estimators, Semiparametric Cox model

Part IV (Nonparametric Forecasting)

Conformal prediction intervals

Prerequisiti

Strongly suggested: Statistics, Probability, Metodi e Modelli per l’Inferenza Statistica, Applied Statistics.

Modalità di valutazione

The course assessment will consist of a written exam (5cfu) and a team project (8 cfu).

The written exam will be taken in one of the dates scheduled by the School within the academic year; it will consist of a theoretical test (around 40 minutes) and 2 exercises (around 80 minutes), to be solved autonomously in an open-book mode, through the use of R software.

At the end of the exam the student will decide whether or not to have their exam evaluated.

The written exam will be evaluated with a score expressed in a scale from 0 to 30, the maximum evaluation being 32/30. The written exam will be passed upon obtaining a score greater than or equal to 18/30. The exam evaluation will account for the degree of clarity of the exposition and for the correctness of methods and computations.

The team project will consist of an analysis of a real dataset, to be conducted in teams of 2 to 4 students, using the models and methods introduced in the course. The team projects will be presented at the end of the course in a seminar during an open workshop that will take place after the end of the semester. Each team will receive an evaluation in a scale from 0 to 30.

The final evaluation of the course will be obtained as a weighted average of the scores obtained by the student in the two parts of the assessment.

During the exam, the students will have to

- Demonstrate the degree of knowledge and comprehension of the key aspects of the course, presenting the used methodologies in a clear and exhaustive way;

- Demonstrate their ability to apply the learned notions to solve exercises and real problems, on any of the topics covered in the course.

Bibliografia

Regina LiuJ. M. PareliusK. Singh, Multivariate Analysis by Data Depth: Descriptive Statistics, Graphics and Inference, Editore: The Annals of Statistics, Anno edizione: 1999, Fascicolo: 27(3):783-858 Note:

A further selection of scientific papers for each topic will be provided by the teachers.

Fortunato Pesarin; Luigi Salmaso, Permutation Tests for Complex Data: Theory, Applications and Software, Editore: John Wiley & Sons, Anno edizione: 2010
Trevor Hastie; Robert Tibshirani; Jerome Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction: Data Mining, Inference, and Prediction, Editore: Springer
Hosmer, D.W., Lemeshow, S., Applied Survival Analysis, Editore: John Wiley & Sons, Anno edizione: 2008
Vladimir Vovk; Alex Gammerman; Glenn Shafer, Algorithmic learning in a random world, Anno edizione: 2005

Forme didattiche

Tipo Forma Didattica

Ore di attività svolte in aula

(hh:mm)

Ore di studio autonome

(hh:mm)

Lezione

28:00

78:00

Esercitazione

22:00

42:00

Laboratorio Informatico

30:00

0:00

Laboratorio Sperimentale

0:00

0:00

Laboratorio Di Progetto

0:00

0:00

Totale

80:00

120:00

Informazioni in lingua inglese a supporto dell'internazionalizzazione

Insegnamento erogato in lingua
Inglese

Disponibilità di materiale didattico/slides in lingua inglese

Disponibilità di libri di testo/bibliografia in lingua inglese

Possibilità di sostenere l'esame in lingua inglese