Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


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: 08.09.2020 - 07.12.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Riku Linna

Teacher in charge (applies in this implementation): Riku Linna

Contact information for the course (valid 05.08.2020-21.12.2112):

Lecturer: Riku Linna, e-mail:

Assistant: Kavya Sreekumar, e-mail:

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    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:

    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 01.08.2020-31.07.2022:

    Examination and computational exercises.

  • Applies in this implementation:

    The course is completed by doing programming assignments and a final exam. The main emphasis on assignments, they contribute 70 %  the exam contributes 30 % to the grade. Minimum requirement to pass is 50 % of the total weighted points from the assignments and the exam. Depending on the Corona virus situation, the exam may be replaced by extra assignments.

  • Valid 01.08.2020-31.07.2022:

    Lectures 10x2h, computer exercises 10x2h, independent studying (lectures, programming, exercise reports), final exam

  • Applies in this implementation:

    Studying for and doing the assignments is estimated to take approximately 75 h.

    Preparation for the exam is estimated to take approximately 20 h. 

    So, together with the lectures and exercise sessions the total estimated workload is 135 h.

    Attendance to lectures and exercise sessions is voluntary.


Study Material
  • Valid 01.08.2020-31.07.2022:

    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.

  • Applies in this implementation:

    Some additional material will be given along the way. This will be specified on the course page.

    The book "Introduction to Probability and Random Processes" freely available online will be used in parts of the course: 

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    Replaces courses CS-E5790/ BECS-114.1100 Computational Science, S-114.100 and S-114.1100.

  • Valid 01.08.2020-31.07.2022:

    The student should have basic programming skills. The programming language Python will be used. First year mathematics. Also recommended: MS-CS2111 Stochastic Processes.



Registration and further information