LEARNING OUTCOMES
After the course you have a good command of selected central concepts and tools in stochastics.
You can program and use algorithms for analysing data and simulating and solving problems related to stochastic processes.
You have a thorough understanding of Monte Carlo-based methods and some of its advanced variants and a fair background for studying Bayesian statistical modelling.
Credits: 5
Schedule: 03.09.2024 - 09.12.2024
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Riku Linna
Contact information for the course (applies in this implementation):
Teacher: Riku Linna (riku.linna@aalto.fi)
Teaching assistants: Alireza Honarvar (alireza.honarvar@aalto.fi), Yejun Zhang (yejun.zhang@aalto.fi)
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
Fundamentals of relevant numerical mathematics, practical tools for data analysis (such as logarithmic binning), generation of random variables from different distributions,
Markov chains, Monte Carlo methods (MCMC, Hamiltonian MC), some of the most important stochastic processes (e.g. Poisson, Gaussian, First-Passage)
applies in this implementation
The purpose of this course is to provide an understanding of fundamental concepts and computational methods of stochastic simulations and models. After completing the assignments the student will have a library of (skeleton) algorithms used in stochastic simulation and an understanding of how they work.
Topics include:
1. Simulating standard probability distributions.
2. Methods of simulating 'non-standard' distributions. Logarithmic binning.
3. Markov processes and stochastic models.
4. Monte Carlo (MC) method and Metropolis sampling.
5. Markov Chain Monte Carlo (MCMC) method; Gibbs and Metropolis-Hastings sampling.
6. Hamiltonian/Hybrid Monte Carlo (HMC) method.
Assessment Methods and Criteria
valid for whole curriculum period:
The final grade is determined by the following weighted sum: Computational assignments (70 %) + examination (30 %). Within computational assignments grading consists of the completed assignments (80 %) + peer reviewing (20 %). If this needs to be modified, it will be agreed upon at the start of the course.
Workload
valid for whole curriculum period:
Lectures 6x1.5 h, computer exercises appr. 7x1.5 h, independent studying (lectures, programming, exercise reports), final exam.
Work load: Contact teaching 20 h + independent work studying for and completing the exercises 80 h + independent work doing the peer reviewing 10 h + preparing for and taking the exam 25 h = 135 h (5 cr).
DETAILS
Study Material
valid for whole curriculum period:
Lecture notes and given articles. Reference books are Mark A. Pinsky, Samuel Karlin: An Introduction to Stochastic Modeling (2011 Elsevier), and Darren J. Wilkinson: Stochastic Modelling for Systems Biology, 2012 CRC Press.
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
SDG: Sustainable Development Goals
3 Good Health and Well-being
13 Climate Action
14 Life Below Water
15 Life on Land
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language: English
Teaching Period: 2024-2025 Autumn I - II
2025-2026 Autumn I - II