Study: Master in Statistics for Data Science (345)
Coordinating teacher: D AURIA , BERNARDO
Department assigned to the subject: Department of Statistics
ECTS Credits: 3.0 ECTS
Students are expected to have completed
An elementary course of Probability and Statistics
Competences and skills that will be acquired and learning results.
To acquire basic rudiments of the theory of stochastic processes.
Modeling real problems through Markov processes and Martingales.
To solve problems using the appropriate stochastic methodologies and techniques.
Description of contents: programme
1. Discrete-time Markov chains
- Definition and basic computations
- Classification of states
- Limiting and stationary distributions
- Limit theorems
- ML estimation of transition probabilities
2. Markov chain Monte Carlo
- The Metropolis-Hastings algorithm
- The Gibbs sampler
- MCMC diagnosis
3. Poisson process
- Inter-arrival times
- Infinitesimal probabilities
- The connection with the uniform distribution
- Thinning and superposition
- Non-homogeneous Poisson processes
4. Continuous-time Markov chains
- Transition function and transition rates
- Long-term behaviour
5. Brownian motion and Gaussian processes
- Brownian Motion
- Transformations and Properties
- Extensions of the Brownian Motion
- Gaussian processes
Learning activities and methodology
Every week there is a class. In each class, the theoretical concepts are usually introduced, numerical and simulated exercises are shown to better understand them and examples of models that can be used in more specific applications are made.
% end-of-term-examination 30
% of continuous assessment (assigments, laboratory, practicals...) 70
Norris, J.R.. Markov Chains. Cambridge University Press. 1997
S.M. Ross. Introduction to probability models. Academic Press. 2007
The course syllabus and the academic weekly planning may change due academic events or other reasons.