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

Computational methods for statistics

Computational methods for statistics

Academic year 2017/2018

• NUMERICAL AND STATISTICAL METHODS FOR FINANCE (ECO0152)
  Corso di studio in 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

After this course the students will be familiar with pseudo-random number generators and with the statistical software R. They will know how to sample an independent and identically distributed  sequence or (pseudo) random number with a given distribution, and will be able to implement a Monte Carlo integration algorithm in R. Moreover, students will learn some of the most common statistical methods  based on sampling strategies (e.g., Bootstrap,  Jackknife,  Bayesian estimation).

Course delivery

Half of the lectures will be devoted to the theoretical aspects of simulation and Monte Carlo Integration and the remaining half to their practical implementation in the R software considering both the related numerical and computational issues. Exercises will be assigned during  lectures and lab sessions.

Learning assessment methods

The exam consists of two parts: the first part is a written exam on theory; the second part is a practical session with R.

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
• Visit the forums