- Docente: Cinzia Viroli
- Credits: 10
- SSD: SECS-S/01
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Statistical Sciences (cod. 8875)
Learning outcomes
Students will learn numerical techniques useful in the context of classical and bayesian estimation.
In particular, students will be able to:
- find maximum likelihood estimates with Newton-Raphson and quasi-Newton methods,
- apply the E-M algorithm to simple probabilistic models,
- evaluate bias and presicion of estimates through resampling techniques,
- use Gibbs samples and Markov Chain Monte Carlo in bayesian estimation.
Course contents
- Numerical techniques for solving nonlinear equations: applications to maximum likelihood method.
- E-M algorithm: definition, properties and variants.
- Introduction to resampling techniques; bootstrap methods for hypothesis testing and confidence intervals; permutation tests.
- Introduction to numerical and Monte Carlo integration techniques.
- Markov Chain Monte Carlo methods for Bayesian estimation: Metropolis-hastings algorithm and Gibbs sampler.
Readings/Bibliography
- G. H. Givens, J. A. Hoeting (2005): Computational Statistics. Wiley & Sons, Hoboken.
- M. L. Rizzo (2008): Statistical Computing with R. Chapman & Hall, Boca Raton.
- Lecture notes
Teaching methods
- Lectures
- Tutorial sessions in computer laboratory
Assessment methods
The learning assessment is composed by a practical exam in computer laboratory lasting 2 hours, followed by an oral examination. The lab test is aimed at assessing the student's ability to use the theoretical tools to analyze real data with R. During the lab exam, students can make use of notes. The lab test consists of 1 or 2 exercises articulated in several questions.
Teaching tools
Lecture notes
Office hours
See the website of Cinzia Viroli