CS-E5795 - Computational Methods in Stochastics D, Lecture, 3.9.2024-9.12.2024
Osion kuvaus
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Please be kindly informed that using Chat GPT in doing assignments in this course is not allowed.
Please note: In order to have your registration for this or any other course accepted in Sisu, the course must be included in your study plan. Check that this is the case and also check that you have the latest version of your study plan in place.
Please also note: Professors or lecturers don't have permission to enrol students in Sisu. So, if you need to register after the deadline for the course in Sisu, please send a message to course-sci@aalto.fi. You can cc me, Riku Linna (riku.linna@aalto.fi), just in case if the people in learning services need a confirmation from me. If registering in Sisu cannot be done right away, send an e-mail to me, and I will add you to MyCourses (provided you have an aalto e-mail).
Lecturer:
Riku Linna (riku.linna@aalto.fi)
Teaching Assistants:
Trung Nguyen (trung.t.nguyen@aalto.fi)
Yejun Zhang (yejun.zhang@aalto.fi)Lectures, Tuesdays 12:15
Lecture hall D/ Y122, "Kandidaattikeskus" (Main Building).
Exercise sessions, Thursdays 10:15
Y429c-d (Linux) - Y429c-d, "Kandidaattikeskus" (Main Building)
While you are welcome to join, attendance is not required. The course is taken by returning weekly assignments and grading two or three assignment submissions weekly, using FeedbackFruits and taking the exam at the end. Deadlines for submission of solutions, peer grading, and feedback can be found under Assignments. Of the exercise points, 80 % of the points come from graded solutions 20 % of the points come from doing the peer grading.
Please note that since the assignments are peer reviewed, unfortunately, you cannot come back next year and return possibly similar/same problems for grading.
Grading The grade is determined by the exercises (appr. 70 %) and the exam (appr. 30 %). Peer grading will constitute 20 % of the exercise points.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.
Literature: 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.
The book Hossein Pishro-Nik, Introduction to Probability and Random Processes, freely available online is a good reference for some parts of the course: https://www.probabilitycourse.com
Prerequisites:
Basic programming skills. The programming language is Python. Jupyter notebook will be used.
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Ranmar RNG Kansio
This is the Ranmarrandom number generator that was commonly used before Mersenne-Twister algorithm was written. After compiling them, one runs Rmarin first and then generates random numbers with Ranmar (see Lecture 1). This is here just if someone should be interested.
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Sep 11: Added one slide (page 20) where correspondence of Box-Muller transformation to the general transformation (slide 10) is shown.
Sep 24: Removed a redundant sentence on slide 37.
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Modified Sep 25, 15:31: In addition to a couple of small changes, two pages (19 and 20) were added to clarify the relation between stationarity, reversibility and detailed balance of Markov chains.
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Edited Oct 8, 3:32 pm: Added a comment in the pseudocode, p. 47.
Edited Oct 9, 5:11 pm: Added something on page 24.
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An outline of what we covered and what is important. I will probably modify this after the last lecture.
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Example exam Kansio
Here's an old exam to give you some idea of what's ahead. You can ignore the first question, since nothing will be asked about random number generators. The questions here do not cover even close to everything that can be asked, of course. But something like this is to be expected: You need to remember some formal stuff to get started with a problem and you need to remember central concepts. First and foremost, you need to understand. There will be some short essay or mathematical questions where you need to know some central concept and be able to use, for example, the Bayes theorem to get a result of a couple of steps. For further info, see 'Exam stuff'.
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Books Kansio
The book Hossein Pishro-Nik, Introduction to Probability and Random Processes, is a useful reference for some parts of the course: https://www.probabilitycourse.com
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= set of problems. Submit your solutions in Exercise 6 (FeedbackFruits).
Edit Oct 11, 10 am: In problem 1. a) "maximises acceptance ratio" was changed to "maximises acceptance probability".
Edit Oct 11, 2:37 pm: In problem 1. a) one more change of "acceptance ratio" to "acceptance probability" and "A" to "alpha".
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= set of problems. Submit your solutions in Exercise 7 (FeedbackFruits).
Edit Oct 17, 11 am: Added a note about grading if epsilon smaller than 0.1 needs to be used.
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Old lecture videos Kansio
At a couple of requests, here's the link to old videos from the corona era. If you can't attend the lectures you should be fine with lecture slides and possibly some bits of the course books. However, if you think watching these old b-movies is useful, feel free to do so at your own risk; there might be some minor errors and some changes have and will be made this year.