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CS-E5795: Computational Methods in Stochastics

Course name Computational Methods in Stochastics
Course code CS-E5795
Abbreviation -
Period I-II
Lecturer Riku Linna

Description

Concrete simulation of problems which have stochastic properties. Methods include mostly different Monte Carlo methods.

Course material

Official material

Lecture slides. Slides are fine considering information but very congested at the same time.

Extra material

Parts of the books Taylor, Karlin (newer edition Pinsky, Karlin): An Introduction to Stochastic Modeling (Academic Press), and Wilkinson: Stochastic Modelling for Systems Biology (CRC Press). Lecture notes and other distributed material.

From MyCourses - The book Hossein Pishro-Nik, Introduction to Probability and Random Processes, is a useful reference for some parts of the course: probabilitycourse.com.

Contents and workload

The course assignments are relatively easy for a master’s level course but the exam is very differently demanding when compared to the returned coding assignments as it is a lot more theoretical in nature.

This course is a two period course since the first period is mostly used as the main learning period and the exam is placed on the exam week of period II. As mentioned above, the coding assignments do not properly prepare for the exam which is A LOT more theoretical in nature. Do pay attention to the lecture notes when preparing for the exam!

Overall workload

Weekly contents

Week Topics
1 Simulating standard probability distributions - Standard introductory week familiarizing students to the procedures of the course. Workload is low.
2 Methods of simulating ‘non-standard’ distributions. Logarithmic binning - Relatively straightforward topic wise, low workload.
3 Markov processes and stochastic models - First more difficult set of topics but topics are very similar to what one would go through in the course Stochastic processes. The assignments are relatively doable but topics may require more time to consider than previous weeks. Moderate to low workload based on how well you remember stochastic processes.
4 Monte Carlo (MC) method and Metropolis sampling - This is mostly a simple introduction to Monte Carlo methods (if you have done the Finnish course MS-C2107: Sovelletun matematiikan tietokonetyöt, you should have the required information) in the context of Poisson-processes. Workload is relatively low but it is vital to understand the concepts for the following weeks.
5 Markov Chain Monte Carlo (MCMC) method; Gibbs and Metropolis-Hastings sampling - Metropolis-Hastings and Gibbs samplers, these methods apply the methods from previous week and relatively hard algorithms are formulated. This is a notable spike in the concepts’ difficulty after the previous weeks and thus the workload can be considered moderately high. However, these are concepts that have been considered in many other courses (CS-E5710: Bayesian Data Analysis, MS-E1654: Computational Inverse Problems for example) so if you have previous experience with these algorithms, the workload is slightly more reasonable.
6 Hamiltonian/Hybrid Monte Carlo (HMC) method (leapfrog method) - This builds upon the week 5 concepts which applies the more simplistic cases from week 5 to more difficult concepts e.g. Hamiltonitan dynamics. These topics are IMMENSELY useful in other applications of computational engineering and thus understanding the methods can be very beneficial in long term. The workload is similar to week 5 as the algorithms stay similar but become a bit more difficult to implement.

Practicalities

Course is graded in 1-5 scale. The grade is determined by the exercises (appr. 70 %) and the exam (appr. 30 %). Peer grading will constitute 20 % of the exercise points. This is subject to change and if it does, then this is discussed during the lectures.

Official prerequisites

MS-C2111: Stochastic Processes. It is officially recommended on the MyCourses page to have at least some programming knowledge. (Python and Jupyter notebooks are used during the course)

Additional prerequisites

This course is relatively fine to take as a bachelor’s level student. If you are Finnish, consider taking MS-C2107: Sovelletun matematiikan tietokonetyöt if it fits your studies. Courses like CS-E5710: Bayesian Data Analysis and MS-E1654: Computational Inverse Problems do help with some of the more difficult topics but these should not considered to be prerequisites to this course.

More like this

Relatively similar to CS-E5710: Bayesian Data Analysis. CS-E5755: Nonlinear Dynamics and Chaos is suggested as a similar but different course during the lectures. Simulation courses (MS-E2155: System Dynamics Simulation, MS-E2150: Discrete Event Simulation) may handle similar topics.

Trivia