Master in Statistics for Data Science (Plan: 386 - Estudio: 345)
EPI
Coordinating teacher: ARRIBAS GIL, ANA
Department assigned to the subject: Statistics Department
Type: Compulsory
ECTS Credits: 3.0 ECTS
Course: 1º
Semester: 1º
Requirements (Subjects that are assumed to be known)
Probability, Programming in R
Objectives
To acquire basic rudiments of the theory of stochastic processes.
Modeling real problems through Markov and Poisson processes.
To solve problems using the appropriate stochastic methodologies and techniques.
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
- Definition
- Inter-arrival times
- Infinitesimal probabilities
- The connection with the uniform distribution
- Thinning and superposition
- Non-homogeneous Poisson processes
4. Continuous-time Markov chains
- Introduction
- Transition function and transition rates
- Long-term behaviour
- Time-reversibility
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.
Assessment System
% end-of-term-examination 40
% of continuous assessment (assigments, laboratory, practicals...) 60