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Scheda Riassuntiva
Anno Accademico 2020/2021
Scuola Scuola di Ingegneria Industriale e dell'Informazione
Insegnamento 055700 - COMPUTATIONAL STATISTICS
Docente Manzoni Andrea
Cfu 8.00 Tipo insegnamento Monodisciplinare
Didattica innovativa 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*AZZZZ055701 - COMPUTATIONAL STATISTICS
055700 - COMPUTATIONAL STATISTICS

Obiettivi dell'insegnamento

This is a course about exploring random systems using computer simulations. Indeed, almost every mathematical model describing systems or phenomena of interest is hampered by uncertainties, although very often uncertain features or inputs are not accounted for.

The goal of the course is to introduce computational tools aiming at: (i) describing uncertainty sources in general systems, with special emphasis on differential models, and (ii) analyzing the impact of uncertainty on systemsoutcomes, in terms of both uncertainty propagation from inputs to outputs, and input parameter estimation from noisy observations.

 


Risultati di apprendimento attesi

Besides the knowledge of theoretical results and numerical methods presented during lectures and Lab sessions, a critical comprehension of the class’ topics is expected by the students at the end of the class, justifying the followed procedures. Attending the course, students are expected to:

  • know and understand how to perform numerical simulation of random processes and sampling methods, and how to tackle uncertainty quantification issues related with steady and unsteady systems;
  • adapt the proposed methodologies to problems of applied interest in Engineering;
  • interpret the results, assessing both accuracy and efficiency of simulation strategies, from both a numerical and a statistical point of view.

Argomenti trattati

The course is organized in theoretical lectures and lab sessions. An additional project must be carried out in the form 5+3 CFU. Lectures will provide the theoretical background; practical Lab sessions will provide algorithms' implementation and examples of application of the considered methodologies by using basic Matlab codes.
 

Part 1. Numerical simulation of random processes and sampling methods

  • Random number generation: inversion method, transformations, rejection sampling. 
  • Gaussian processes. Karhunen-Loève expansion.
  • Monte Carlo methods, estimates, error. Multi-level (or multi-fidelity) Monte Carlo methods.
  • Variance reduction techniques.

Part 2. Sensitivity analysis and forward Uncertainty Quantification

  • Sensitivity analysis of multiple parameters: one-at-a-time, elementary effect methods, variance-based methods.
  • Surrogate models or emulators: polynomial chaos expansions, reduced-order models.
  • Uncertainty propagation through Monte Carlo methods. Application to differential models.

Part 3. Data assimilation and inverse Uncertainty Quantification

  • Statistical inverse problems: a Bayesian setting for parameter estimation.
  • Monte Carlo Markov Chain methods. Application to differential models.
  • Data assimilation: Kalman filters and particle filters. Application to differential models.

 


Prerequisiti

The course targets students following either a Computational Science and Engineering or an Applied Statistics track.
Students are required to have a solid background in Statistics, Probability, Numerical Analysis.
A solid background in Matlab programming is assumed.


Modalità di valutazione

In the 5CFU form, the exam consists of an oral test, covering the content of both theoretical lectures and practical Lab sessions.

In the 5+3CFU form, the grade of the oral test is 5/8 of the final grade, and a
n additional project dealing with some of the class topics, chosen among a list of proposed titles, has to be carried out, in teams of 1 to 3 students.

The project will consist of the use, adaptation or extension of some of the methods presented during the course, to a case of interest, starting, e.g., from the critical analysis of a recent scientific paper. Projects will be presented at the end of the course in short seminars during an open workshop that will take place after the end of the semester. The presentation of the project provides 3/8 of the final grade.

 

The course will be based on a selection of chapters of the following books, class notes, and some selected scientific papers provided:


Bibliografia
Risorsa bibliografica facoltativaJochen Voss, An Introduction to Statistical Computing. A Simulation-based Approach., Editore: . John Wiley & Sons, Anno edizione: 2014
Risorsa bibliografica facoltativaRalph C Smith, Uncertainty Quantification: Theory, Implementation, and Applications, Editore: SIAM, Anno edizione: 2013
Risorsa bibliografica facoltativaJari Kaipio, Erkki Somersalo, Statistical and Computational Inverse Problems, Editore: Springer, Anno edizione: 2005
Risorsa bibliografica facoltativaMark Asch, Marc Bocquet, Maelle Nodet, Data Assimilation. Methods, Algorithms, and Applications, Editore: SIAM, Anno edizione: 2016

Forme didattiche
Tipo Forma Didattica Ore di attività svolte in aula
(hh:mm)
Ore di studio autonome
(hh:mm)
Lezione
34:00
78:00
Esercitazione
16:00
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
Disponibilità di supporto didattico in lingua inglese
schedaincarico v. 1.6.5 / 1.6.5
Area Servizi ICT
16/06/2021