Project 4 - Probabilistic Modeling#
Due 14 Dec 23
Project 4 emphasizes probabilistic models. We’ve done work with counting statistics (flipping coins and rolling die). We’ve modeled radioactive decay and decay chains. We’ve developed Monte Carlo simulations to do integrals and to model different systems. In this project, you are free to choose a particular probabilistic model and apply it to a new physics situation of your choosing. You may be creative in your choice of model and situation, but you must be able to justify your choices.
You also have now done 3 of these projects, so you should be able to decide for yourself what you want to use from this course module.
What do you need to do?#
Think about different systems you have seen or read about that have probabilistic individual outcomes but are part of a collection (a multiple particle system). For example, as we saw the random decay of an atom can be modeled this way to say something about the decay of a sample. It might not seem obvious, but a leaf breaking off a tree in a light breeze can be modeled as a probabilistic process. You might also consider using a Monte Carlo simulation to model a system. We’ve used them to perform integrals, but also to show the behavior of spins in a magnetic field. Monte Carlo simulations have wide applicability.
Choose a physical system that can be modeled using a probabilistic model
Describe the physical system and how your probabilistic model can be used to explore it.
Develop a series of questions that you can answer using your model
Develop a investigation that answers those questions using analytical and numerical approaches
Set up and perform the analysis
Ensure you present your results in a way that is clear
Earning extra credit for more explorations#
Monte Carlo simulations take a long time to run, so most of these are not required. If you want to explore these, you can earn extra credit.
Explore parameter effects on your model
Explore the effects of performing the Monte Carlo poorly (e.g., not enough points, not enough data, etc.)
Perform a project with a 2D Monte Carlo simulation
Submitting your work#
You will upload your work to D2L. It should be a single PDF of your work. If you also write code, please submit the associated files as well. If you do all of this in a Jupyter notebook, please export the notebook as a PDF and submit the notebook and PDF file. If you have any questions, please ask. We want you to enjoy working on these problems.