Probabilistic weather modeling using Markov chains, applied to real historical weather data from Seattle. Built as the final project for a Probabilistic Methods course.
- Builds a transition matrix from historical daily weather labels (rain, sun, snow, fog) — each entry is the conditional probability of transitioning from one state to the next.
- Simulates the Markov chain for varying numbers of steps (25 to 100,000) using Monte Carlo sampling.
- Measures convergence by comparing simulated transition matrices against the reference matrix derived from data, using element-wise absolute error heatmaps and the Frobenius norm.
The analysis shows how quickly the simulated distribution converges to the empirical one as the number of Monte Carlo iterations grows.
The Frobenius norm drops sharply between 250 and 2,500 iterations and stabilises beyond 25,000.
Transition graph (conditional probabilities from real data):
Error heatmaps (simulated vs. real transition matrix, 25 → 100,000 iterations):
The notebook downloads the dataset automatically via kagglehub (Seattle weather dataset by petalme).
nix-shell pm_project.nix
# a Jupyter server starts automatically; open the URL printed in the terminalpip install numpy pandas matplotlib seaborn kagglehub graphviz jupyter
jupyter notebook project.ipynb| File | Description |
|---|---|
project.ipynb |
Main notebook — data loading, transition matrix, simulation, analysis |
pm_project.nix |
Reproducible Nix dev shell (Python 3.13 + Jupyter) |
figures/ |
Output plots: transition graph (SVG), Mermaid diagram, error heatmaps |
Project_Report_PM.pdf |
Written report |