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Stochastic Modelling and Processes - Spring 2025

Repository for SMP1-S25 at VIA

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Course information

  • Course responsible: Associate Professor Richard Brooks, rib@via.dk
  • 5 ECTS (European Credit Transfer System), corresponding to 130 hours of work
  • 11 sessions, each with a duration of 4 lessons, starting in week 6
  • Bachelor level course - the course is academically challenging working on problems independently.
  • Grade: 7-step scale
  • Type of assessment: 4-hour written exam (see exam description in the menu to the left)
  • Recommended prerequisites: In "Sessions" in the left menu, a dedicated entry is made for prerequisites.

:fontawesome-solid-vector-square:{ .fa-vector-square} Lectures and course organization

The course is scheduled to start in week 6 and will be held on Tuesdays from 12:45 to 16:05 in room C04.16. In general, each session is made up of four activities:

  1. At the beginning of each session, there will be a short recap of the previous session.
  2. We then go through the exercises from the previous session.
  3. We will go through the theory of the current session.
  4. After classes, and before the next session, you will have to solve exercises from the current session.

This then loops back to (1) at the beginning of the next session.

There are no mandatory assignments, but it is highly recommended to work on the exercises for each session. No instruction is provided for the exercises so you will have to work on them on your own or form study groups.

Course content and learning objectives

Stochastic Modelling and Processes is the art of making sense of randomness in the world around us. We examine probability theory, finding the tools to describe and analyse random systems mathematically. You'll learn about random variables — their mean, variance, and the distributions that define them — and learn how these concepts power everything from decision-making to machine learning.

Learning Objectives

  • Probability: Understand the fundamental concepts of probability theory, including experiments, sample spaces, independence, conditional probability, and Bayes' theorem. Learn to approach random systems methodically using probabilistic reasoning.
  • Random Variables: Describe and analyse random systems through random variables. Understand their characteristics, including mean, variance, standard deviation, and commonly used distributions like normal, binomial, and Poisson.
  • Point Estimation: Learn techniques to estimate population parameters from sample data and evaluate the quality and reliability of these estimates.
  • Statistical Intervals: Construct and interpret confidence intervals for population parameters. Learn to assess the precision of estimates and their implications for statistical inference.
  • Hypothesis Testing: Explore the principles of hypothesis testing. Learn to formulate null and alternative hypotheses, compute and interpret p-values, and make informed decisions based on statistical evidence.
  • Regression Analysis: Investigate relationships between variables using regression models. Understand how to fit, interpret, and assess the quality of regression models for real-world data.
  • Stochastic Processes: Model and analyse systems that evolve over time using stochastic processes, including applications of Markov Chains for dynamic systems.
  • Python for Statistical Modelling: Gain hands-on experience with Python for data analysis, simulating random variables, conducting statistical tests, and visualizing statistical data to reinforce theoretical understanding.
  • Critique and Evaluate Statistical Models: Develop the competence to critically assess statistical models and results. Identify sources of error, critique experimental designs, and propose improvements for better reliability.

But it's not just about theory. You'll get hands-on with Python, simulating randomness, running statistical tests, and exploring applications of stochastic models. By the end, you’ll not only understand how to model uncertainty but also how to use it to make informed predictions and decisions.

Resources

ASPE: Montgomery, D.C. & Runger, G.C.. Applied Statistics and Probability for Engineers, 7th edition. All references are to chapters or exercises (found in the end of the book). Solutions to all exercises from the book are uploaded. You need to retrieve a copy however you usually retrieve books.

Non-session specific resources such as the exercises from the book, solutions, old exam cases, etc. can be found her:

General Resources SMP

This folder is always accessible in the menu to the left.

The Wiseflow code for all flows that are used during the course is always 0000. This is not the code for the actual exam in June, though.

The course is loosely built up around H. Pishro-Nik's https://www.probabilitycourse.com/

I have compiled and uploaded all session from January 2021 to YouTube. The link below will take you to a playlist containing all 10 sessions (theory only)

Stochastic Modelling 2021 – All sessions

Make sure you install a working version of Jupyter Notebook and Python version 3.7 or higher. The easiest way to install Python and Jupyter is using Anaconda Distribution. You can choose whichever framework you want to work in as long as it can handle Jupyter Notebooks. Installing VS Code with a Jupyter Notebook extension seems to be a popular choice.

Historical Notes

Stochastic Modelling and Processes was first offered in 2014 and has been scheduled 1–2 times per year since. The course responsible is Richard Brooks (RIB) and has been the only lecturer teaching the course.

Grade Distribution 2024 (ordinary exam only)

Grade Count
12 3
10 8
7 7
4 5
02 4
00 6
-3 1