STAT447 - Coursework and Final Project

This repository contains coursework and the final project for STAT 447. The final project focuses on leveraging conjugacy in Dirichlet Process Poisson Mixture Models.

Directory Structure

data

Contains the raw data files used for analysis, across homework and projects.

final_project

This folder includes all files related to the final project:

cleaned_crash_data.csv: Processed and cleaned crash data used in the analysis.
dirch_appx.png: Visualization of the finite approximation of the Dirichlet process.
post_box.png: Boxplots of posterior rate parameters.
post_comp.png: Posterior predictive versus observed data comparison.
posterior_results.RDS: Saved RDS file of the posterior results.
posterior_sampleframe.RDS: Sample frame from the posterior.
posterior_sims.RDS: Simulated posterior draws.
results.tex: LaTeX file of the posterior parameters and weights.

finished_homework_pdfs

Completed homework assignments in PDF format.

homework_rmds

R Markdown files for the homework assignments.

images

Images used in the reports and visualizations.

notes_and_utils

Notes and utility scripts used throughout the coursework.

Getting Started

Necessary R packages:

install.packages(c("dirichletprocess", "ggplot2", "latex2exp", "dplyr", "lubridate", "readxl", "tidyr", "pbapply", "hexbin", "scales", "knitr", "kableExtra"))

Run the R scripts: Navigate to the final_project directory and run the R scripts to reproduce the analysis and visualizations.

Copyright and Licensing

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. You may not use this work for commercial purposes. You may share this work with proper attribution, but you may not alter, transform, or build upon this work without express permission from the author.

For more details about the license, see the Creative Commons License.

If you wish to cite this work for any purpose, please use the following bibtex citation style:

@misc{hewlett2024stat447,
  author = {Caden Hewlett},
  title = {Leveraging Conjugacy in Dirichlet Process Poisson Mixture Models},
  year = {2024},
  howpublished = {\url{https://github.com/cadenhewlett/STAT447}},
  note = {STAT 447 Final Project, University of British Columbia}
}

Project Description

This is an overview of the project. Full details are in main.pdf.

Introduction

This project presents a non-parametric approach to the Gamma-Poisson (GP) model framework using weekly aggregation of daily crash count data from the Chicago Police Department. The main goal is to integrate the GP Bayesian Model with the dirichletprocess R package, which does not have an out-of-the-box solution for this setup.

Methods

The project utilizes the stick-breaking process to define the Dirichlet Process Mixture Model (DPMM) and implements a custom mixing distribution for the Gamma-Poisson conjugate pair.

Results

The results include posterior parameter estimates, cluster assignments, and predictive densities. The analysis demonstrates the effectiveness of the DPMM in identifying varying rates of crash counts.