Laurea Magistrale (M.Sc.) in Stochastics and Data Science

Computational methods for statistics

Computational methods for statistics

Academic year 2018/2019

• NUMERICAL AND STATISTICAL METHODS FOR FINANCE (ECO0152)
  Quantitative Finance and Insurance

Sommario del corso

• Course objectives
• Results of learning outcomes
• Course delivery
• Learning assessment methods
• Program
• Suggested textbooks and readings
• Notes
• Teaching tools

Course objectives

This course aims at introducing the students with computational statistics methods. The program includes some computationally intensive methods in statistics, such as Monte Carlo methods, bootstrap, and permutation tests. An important part of the course will be devoted to practicals: all the methods discussed during the course will be will be implemented in the R software.

Results of learning outcomes

Knowledge and understanding 
Basic knowledge of Monte Carlo simulation techniques for statistical models; basic knowledge of the language R/Matlab.

Applying knowledge and understanding 
Ability to implement a Monte Carlo simulation of a statistical model using the language R/Matlab.

Making judgements 
Students will be able to discern the different aspects of  Monte Carlo simulations  method applied to statistical problems.

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/Matlab.

Learning skills 
The skills acquired will give students the opportunity of improving and deepening their knowledge of the different aspects of Monte Carlo simulation for Statistical problem using the language R/Matlab.

Course delivery

This course is borrowed from the simulation module (6 creditis) of the course   (NUMERICAL AND STATISTICAL METHODS FOR FINANCE (ECO0152)  of the Mater in Quantitative Finance and Insurance. The two modules, Statistics and Simulations, of the course Numerical and Statistical Methods for Finance are delivered in parallel. Students have to follow only the Lectures on Simulations. These are mainly devoted to the theory and methods for Monte Carlo simulation.

The course Numerical method for Statistics (i.e. the Simulation module of ECO0152)  is  48 hours long (taught classes) with the following subdivision: 18 hours devoted to theory and method; 8 hours of exercises; 12 hours of practical sessions on the computer with the language R/Matlab; exercises will be assigned during the course

Learning assessment methods

The exam consists of two parts:

1) One or two exercises on the topic simulation/integration. Students will be provided with a mock exam, moreover during the course two or three exam-like-exercises  will be discussed. The maximum score for the exercise is 25/30 

2) An exercise on  the software R/Matlab. The student will be asked to comment or to draft an R/Matlab-script. The maximum score for the software exercise is 5/30

Program

• Introduction to the R statistical software.
• Pseudo-random number generator. Linear congruential generators.
• Methods for Generating Random Variables: the inverse transform method, the acceptance-rejection method, the transformation methods.
• Monte Carlo integration methods.
• Variance Reduction, the importance sampling (sampling importance resampling) and the stratified sampling.
• Monte Carlo methods in Inference in a Bayesian and frequentist framework.
• Bootstrap and Jackknife.
• Permutation Tests for Equal Distributions.

1. Rizzo, M.L. (2015) "Statistical Computing with R  (Second Edtion)" -- Chapman & Hall/CRC The R Series.
2. Ross. S.M. (2006) "Simulation 4th edition" -- Academic Press.
3. Jones, O., Maillardet, R. and Robinson A. (2009). "Introduction to scientific programming and simulation usig R" -- Chapman and Hall/CRC;

Class schedule

Note

Class schedule available here.

• Teaching materials
• Exams and finals
• Go to Moodle
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