Simulation

Code:

M4148

Acronym:

M4148

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2021/2022 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Computational Statistics and Data Analysis

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:ECAD	11	Study plan since 2021/2022	1	-	6	42	162

Teaching language

Suitable for English-speaking students

Objectives

It is intended that the students learn the paradigm of computational simulation based on Monte Carlo methods, namely MCMC, as well as the principles of numerical linear algebra, in a framework of critical application as well as their application in interdisciplinary areas.

Learning outcomes and competences

The student should be able to:

- Know and apply the fundamental methods of numerical linear algebra for linear systems. To know the issues concerning convergence, conditioning and errors control, algorithms and computational implementation.

- Know and apply the principles of generation of random variables and integration of Monte Carlo, with results analysis and control of the variance. Understand and apply Monte Carlo methods via Markov Chain (MCMC).

- Apply critically the studied methods to selected case studies of interdisciplinary areas.

Working method

Presencial

Program

Systems of Linear Equations: direct methods (LU factorization and Cholesky decomposition), iterative methods (Jacobi and Gauss-Seidel). 

Introduction to statistical simulation and computation. Comprehensive hands-on excursion of Monte Carlo methods: from random number generation algorithms and Monte Carlo integration, to Markov Chain Monte Carlo. Metropolis-Hastings and Gibbs algorithms, including convergence monitoring.

Mandatory literature

William Ford; Numerical Linear Algebra with Applications Using MATLAB, AP Elsevier, 2015. ISBN: 978-0-12-394435-1
Kroese Dirk P.; Handbook of monte carlo methods. ISBN: 978-0-470-17793-8
Robert Christian P.; Introducing monte carlo methods with R. ISBN: 978-14419-1575-7

Complementary Bibliography

Kenneth Lange; Numerical analisys for statisticians. ISBN: 0-387-94979-8

Comments from the literature

Other Bibliography under Springer Link available at FCUP

Teaching methods and learning activities

Lectures TP organized in accordance with the syllabus and the intended outcomes to present and illustrate the topics. Problems / Projects with strong laboratorial computation component using (Matlab, R, Python). The curricular unit has a strong practical component and classes with computers are essential. The computational projects allow the consolidation and critical application of the syllabus topics.

Software

Matlab /Octave
R
Python

keywords

Physical sciences > Mathematics > Applied mathematics > Numerical analysis
Physical sciences > Mathematics > Applied mathematics
Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Prova oral	30,00
Teste	30,00
Trabalho escrito	40,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Apresentação/discussão de um trabalho científico	1,00
Estudo autónomo	70,00
Frequência das aulas	38,00
Trabalho escrito	3,00
Elaboração de projeto	25,00
Trabalho laboratorial	25,00
Total:	162,00

Eligibility for exams

40% in all the evaluation components (exam, oral presentation, report)

Calculation formula of final grade

Arithmetic mean of the classification in the 2 modules  : numerical linear algebra (AN) and simulation (S).

Final classification AN : 0.4 T+ 0.3 O + 0.3 R,

Final classification S : 0.2 T + 0.3 O + 0.5 R,

T – Computational test

O – oral presentation + discussion

R- Report ( including the computacional part)

At ER the final exam (E) replaces T in the formula.

Minimum mark in each component T, E, O, or  R  is 40%. 

Any component not  concluded in the schedule  and/or established conditions is considered as not performed.

Examinations or Special Assignments

n.a.

Special assessment (TE, DA, ...)

n.a.

Classification improvement