Bonus Assignment 2
Find an Application of Markov Chains
Application of Markov Chains
Introduction
Markov chains appear in many real-world applications. Below are a few articles I found online that are fun and accessible to read:
- First Links in the Markov Chain
- Decoding NBA Tactics: Using Shot Zone Data and Markov Chains for Game Simulation
- Markov Chains and Musical Composition
- Wikipedia: Examples of Markov Chains
Note that Markov chains are among the simplest mathematical models, so they are often used as toy models for much more complicated situations. For example, if you want to analyze literature using a Markov chain (as in the first link), you must make many simplifying assumptions about language. Similarly, if you want to forecast weather using Markov chains, empirical transition probabilities may fail to account for the current weather conditions.
Despite these limitations, Markov chains still provide useful insights. Moreover, once you understand where the model breaks down, you may be motivated to improve it using more advanced mathematics and additional parameters, which is a great reason to learn more math!
Assignment
This assignment consists of two parts.
- Part 1: Propose a model using a Markov chain that is relevant to your daily life, interests, or hobbies, and explain your reasoning. In most cases, you will need to simplify the situation.
- For example, if you want to model what you eat for dinner each day, you might design a transition matrix that approximates how your choices depend on previous meals.
- Part 2: Simulate your model and perform a simple analysis.
- For instance, you might compare your simplified model with actual data and discuss possible reasons for the differences.
- As another example, you could run a long-term simulation and explain any insights you gain from the steady-state behavior or so.
- For instance, you might compare your simplified model with actual data and discuss possible reasons for the differences.
You may use any programming language for simulations, or you may use the visualization tools on our course website (note that these have some limitations). If you have trouble with simulations, feel free to ask me, your classmates, or use AI tools for assistance.
Submission
- Upload your article to the Canvas assignment Bonus Assignment 2. The format can be anything (DOCX, PDF, plain text, etc.).
- Also post your article as a comment in the Canvas Discussion Bonus Assignment 2 so that your classmates can read it.
Grading
- +1% bonus for completing Part 1.
- +1% additional bonus for completing Part 2.
If you want a quick bonus point, I suggest completing only Part 1 with a simple model.