79192 - Computational Statistics

Learning outcomes

The student will learn computational techniques useful in the context of classical and bayesian estimation. In particular, the student will be able to: - find estimates for one or more parameters using iterative algorithms; - evaluate the bias and the precision of the estimates using resampling methods. The student will be able to implement all the computational techniques studied during the course with the statistical software R. Furthermore, the student will be able to perform real data analyses in a critical way in terms of both choice of the best technique to apply and interpretation of results.

Course contents

Introduction to computational statistics and R programming.

Random Variable Generation. Uniform simulation, the inverse transform, general transformation methods, discrete distributions.

Monte Carlo Integration. Introduction, classical Monte Carlo integration. Importance sampling.

Monte Carlo Optimization. Introduction, numerical optimization methods, stochastic search (basic solutions, stochastic gradient methods, simulated annealing).

[Tentative] Bootstrapping. Introduction, parametric and nonparametric bootstrap. 

Readings/Bibliography

• Robert, C. & Casella, G. (2010). Introducing Monte Carlo Methods with R. New York: Springer-Verlag.

• Efron, B. & Tibshirani, R. J. (1993). An introduction to the bootstrap. London: Chapman & Hall/CRC.

Teaching methods

• Conventional lectures

Assessment methods

The exame is comprised of a set of open questions and/or practical exercises to be solved using the software R.

The final mark of the "Numerical Analysis" course is defined as the arithmetic mean of the marks obtained in the test for the Numerical Analysis module and a written exam for the Computational Statistics module.

Teaching tools

Additional material provided by the teacher (iol.unibo.it)

Office hours

See the website of Saverio Ranciati