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Course: 2022/2023

Simulation in probability and statistics

(18284)

Bachelor in Applied Mathematics and Computing (Plan: 433 - Estudio: 362)

Coordinating teacher: CASCOS FERNANDEZ, IGNACIO

Department assigned to the subject: Statistics Department

Type: Compulsory

ECTS Credits: 3.0 ECTS

Course: 4º

Semester: 2º

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

Link to document

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

100% of the course grade will be obtained by continuous evaluation:

- Simulation project: 35%
- Classroom presentation of the simulation project: 10%
- Resampling project: 25%
- Classroom problems: 30%

The students that do not follow the continuous evaluation will be allowed to write a final exam with a total weight of 60%. 

Any student that has not followed the continuous evaluation process has the right to take an extraordinary exam with a total weight of 100% of the course grade. Alternatively, she/he can complete a Simulation project (35%) with its presentation (10%) and a Resampling project (25%) with its presentation (5%) having a total weight of 75%.

% 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.

Go to the detailed contents

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