Bayesian Analysis of Concrete Compressive Strength

This project applies Bayesian linear modeling techniques to the Concrete Compressive Strength Dataset from the UCI Machine Learning Repository. The primary objective is to analyze the relationship between material composition and compressive strength using probabilistic inference.

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📘 Table of Contents

• Bayesian Analysis of Concrete Compressive Strength
  • 📘 Table of Contents
• 🏗️ Concrete Compressive Strength Dataset – Introduction
  • 📊 Dataset Summary
  • 🧪 Features (Ingredients in kg/m³):
• 📦 Environment Setup Guide (Windows 10/11)
  • ✅ 1. Install TDM-GCC (C++ Compiler)
    • ➤ Steps:
    • ➤ Verify:
  • ✅ 2. Set Up Your Python Environment
    • ➤ Create a virtual environment (with uv):
  • ✅ 3. Install Required Python Packages

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🏗️ Concrete Compressive Strength Dataset – Introduction

The Concrete Compressive Strength dataset is a widely used benchmark for regression modeling, sourced from the UCI Machine Learning Repository. It contains experimental data on how the proportions of different concrete ingredients affect the material’s strength. Below is a typical setup used in compressive strength testing of concrete cylinders:

Figure: Compression test configuration for a concrete cylinder
Source: ResearchGate - Compression Test Configuration

📊 Dataset Summary

• Objective: Predict the compressive strength (in MPa) of concrete based on its ingredient mix.
• Records: 1,030 observations
• Features: 8 numerical input variables + 1 target
• Target: Concrete compressive strength (MPa)

🧪 Features (Ingredients in kg/m³):

Feature	Description
Cement	Cement content
Blast Furnace Slag	Supplementary cementitious material
Fly Ash	Alternative cementitious material
Water	Water content
Superplasticizer	Chemical additive to improve flow
Coarse Aggregate	Gravel or crushed stone
Fine Aggregate	Sand
Age	Curing time in days

• Target: Strength – compressive strength of concrete after curing for 90 days.

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📦 Environment Setup Guide (Windows 10/11)

This guide walks you through installing the necessary tools to run Bayesian models using PyMC with compiler and performance support on a Windows system.

✅ 1. Install TDM-GCC (C++ Compiler)

PyMC uses PyTensor as a backend that benefits from C compilation. You'll need a working g++ compiler.

➤ Steps:

1. Download the "TDM-GCC x64 for 64-bit" installer. Download from here
2. Run the installer:
   • Choose TDM-GCC 10.3.0-2.exe (default is fine)
   • Keep all components selected
   • Install to: C:\TDM-GCC-64\ (or leave default)

➤ Verify:

Open Command Prompt and run:

g++ --version

You should see something like:

g++ (tdm64-1) 10.3.0

✅ 2. Set Up Your Python Environment

We recommend using uv or venv to create a clean workspace.

➤ Create a virtual environment (with uv):

uv venv .venv

✅ 3. Install Required Python Packages

Install PyMC and performance libraries:

uv add pymc arviz numba pytensor

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