Sadat Mahmud - Car Price Prediction Using Bayesian GLM

Car Price Prediction Using Bayesian GLM

Advanced Bayesian Data Analysis Project | TU Dortmund | 2024

Quick Summary

We built and compared three Bayesian regression models using GLMs to predict car prices based on a rich dataset of 205 cars. We used brand indicators (BMW, Audi, Toyota), technical specs, and fuel type as predictors — all modeled using Bayesian methods with informative priors and evaluated via Bayes Factors and WAIC.

Tools & Techniques

Language: R (v4.2.2)

Libraries: brms, rstan, loo, ggplot2, dplyr

Model Type: Bayesian GLM

Evaluation: Bayes Factor, WAIC, Posterior Predictive Checks

Models Developed

We built 3 models focusing on different car brands BMW, AUDI, and TOYOTA

BMW

Best performing model.
Key predictors: BMW, engine size, car width, curb weight, horsepower.
Bayes Factor and WAIC showed strong performance over others.

AUDI

Moderate performance .
Engine size, horsepower, and peak RPM had strong positive effects .

TOYOTA

Focused on Toyota brand.
Slightly lower prediction strength compared to BMW model.

Population-Level Effects for BMW

Population-Level Effects for AUD

Population-Level Effects for TOYOTA

Model Evaluation Highlights

Model 1 (BMW) had:
Lowest WAIC: 196.4
Strong Bayes Factor advantage over others
🔄 Posterior predictive checks confirmed the robustness
📉 Residual plots were analyzed for model diagnostics

Key Takeaways

Data preprocessing (one-hot encoding, standardization) was crucial
Bayesian priors bring interpretability and regularization
Engine size and fuel type consistently influenced prices
Model validation with WAIC and Bayes Factor helped in fair selection

Reflection

This project taught us not only how to model but how to think in terms of uncertainty. It deepened our understanding of Bayesian inference and how model diagnostics and prior choices shape trustworthy conclusions.

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