Checking date: 30/05/2022


Course: 2022/2023

Simulation in probability and statistics
(18284)
Study: Bachelor in Applied Mathematics and Computing (362)


Coordinating teacher: CASCOS FERNANDEZ, IGNACIO

Department assigned to the subject: Statistics Department

Type: Compulsory
ECTS Credits: 3.0 ECTS

Course:
Semester:




Requirements (Subjects that are assumed to be known)
Probability (Year 2 - Semester 2) Statistics (Year 3 - Semester 1) Stochastic Processes (Year 4 - Semester 1) - at least partial knowledge
Skills and learning outcomes
Description of contents: programme
1. Random numbers (Monte Carlo tecniques) 1.1 Probability and inference refresher 1.2 Statistical validation techniques 1.3 (Pseudo)random number generation 1.4 Approximation of probabilities and volumes 1.5 Monte Carlo integration 2. Simulating random variables and vectors 2.1 Inverse transform 2.2 Aceptance-rejection 2.3 Composition approach 2.4 Multivariate distributions 2.5 Multivariate normal distribution 3. Discrete event simulation 3.1 Poisson processes 3.2 Gaussian processes 3.3 Single- and multi-server Queueing systems 3.4 Inventory model 3.5 Insurance risk model 3.6 Repair problem 3.7 Exercising a stock option 4. Efficiency improvement (variance reduction) techniques 4.1 Antithetic variables 4.2 Control variates 4.3 Stratified sampling 4.4 Importance sampling 5. MCMC 5.1 Markov chains 5.2 Metropolis-Hastings 5.3 Gibbs sampling 6. Introduction to the bootstrap 6.1 The bootstrap principle 6.2 Estimating standard errors 6.3 Parametric bootstrap 6.4 Bootstrap Confidence Intervals 6.5 Bootstrap Hypothesis Tests
Learning activities and methodology
- Lectures and problem sessions with a computer: introducing the theoretical concepts and developments with examples, and solving problems: 25 on-site hours - Homework: 49 non on-site hours - Evaluation sessions (continuous evaluation and final exam): 5 on-site hours - Specific exam preparation: 49 non on-site hours
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100
Calendar of Continuous assessment
Basic Bibliography
  • Bradley Efron, Robert Tibshirani. An introduction to the Bootstrap. Chapman & Hall. 1993
  • Sheldon M. Ross. Simulation. Academic Press. 2013 (5th ed)
Additional Bibliography
  • Christian P. Robert, George Casella. Introducing Monte Carlo methods with R. Springer. 2010
Detailed subject contents or complementary information about assessment system of B.T.

The course syllabus may change due academic events or other reasons.