Master in Statistics for Data Science (Plan: 386 - Estudio: 345)
EPI
Coordinating teacher: NIÑO MORA, JOSE
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
The course aims to develop the following competences:
1) Capacity to formulate basic stochastic process models (Poisson, Markov chains, Brownian motion) in diverse applications;
2) capacity to analyze such models based on an understanding of their fundamental properties;
3) capacity to investigate numerically such models using software.
1. The Poisson process.
1.1 Introduction and motivation; interarrival and waiting time distributions; conditional distribution of the arrival times.
1.2 Extensions and applications; nonhomogeneous Poisson process; compound Poisson process; conditional Poisson process.
2. Markov chains
2.1 Introduction and motivation; discrete-time Markov chains; Chapman-Kolmogorov equations and classification of states; limit theorems.
2.2 Transitions among classes; applications; reversibility; semi-Markov chains.
2.3 Continuous-time Markov chains; birth and death processes; Kolmogorov equations; limiting probabilities; uniformization.
3. Brownian motion
3.1 Introduction and motivation; hitting times, maximum variable and arc sine laws; variations on Brownian motion.
3.2 Brownian motion with drift; diffusion equations; applications.
Learning activities and methodology
Theoretical-practical classes with web-based supporting material. Computational sessions with numerical software. The teaching methodology will have an eminently practical approach, being based on the analysis and solution of stochastic process models arising in diverse application areas.
Assessment System
% end-of-term-examination 0
% of continuous assessment (assigments, laboratory, practicals...) 100
