Stochastic Simulation

Course manual 2025/2026

Course content

The course builds on the mathematical foundations of probability theory while putting the emphasis on the tools used most often in computer simulations. Our main tool of study are the simulations themselves, therefore the study procedure includes a significant amount of programming. In particular we focus on the following topics:

1. Elements of probability theory
2. Random numbers
3. Statistical analysis of data and error estimation
4. Hypothesis testing and validation of simulation data
5. Variance reduction techniques
6. Discrete event simulations
7. Queuing theory
8. Random walks and Wiener process
9. Monte Carlo and Metropolis methods
10. Importance sampling
11. Simulated annealing
12. Uncertainty quantification

Study materials

Literature

• Sheldon M. Ross, 'Simulation', 5th edition

Software

• Python

Objectives

• Justify the selection of a probability distribution to model a real-world stochastic process
• Formulate appropriate hypothesis tests to determine whether a simulation model's output is statistically consistent
• Identify appropriate sampling techniques based on dimensional constraints
• Implement simulations of fundamental stochastic processes using Monte Carlo and Markov chain techniques
• Develop a (simple example) stochastic computational model based on real-world data

Teaching methods

• Lecture
• Computer lab session/practical training
• Working independently on e.g. a project or thesis
• Self-study

 Lectures will introduce core theoretical concepts through active learning. The computer lab sessions will provide practical exercises and examples to help complete the assignment tasks. The final assignment will require students to synthesize and apply all learned skills to a real-world, open-ended problem.

Learning activities

Attendance

This programme does not have requirements concerning attendance (Ter part B).

Assessment

Inspection of assessed work

The manner of inspection will be communicated via the digitial learning environment.

Assignments

Students must work in a team of three persons on these assignments. Assignments will be graded individually based on student contributions.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Contact information

Coordinator

• dr. Vivek Sheraton Muniraj