Statistical-Inference

Implementations of modern statistical methods from classical and frequentist theory in Python.

This repository showcases clean, practical implementations of statistical techniques — from foundational methods to real-world applications in data science, A/B testing, and predictive modeling.

Topics

statistics, statistical-inference, frequentist-statistics, bootstrap, empirical-bayes, james-stein, hypothesis-testing, survival-analysis, lasso, shrinkage, machine-learning, pycaret, statsmodels, statistical-learning

Repository Structure

Statistical-Inference/
├── src/                          # Core reusable modules
│   ├── bootstrap.py              # Bootstrap resampling, confidence intervals, percentile methods
│   ├── hypothesis_testing.py     # Classical tests, p-values, multiple testing correction
│   ├── empirical_bayes.py        # Shrinkage estimators, James-Stein, empirical Bayes methods
│   ├── shrinkage.py              # Ridge, Lasso-related shrinkage techniques
│   ├── lasso.py                  # LASSO regression, coordinate descent, regularization paths
│   └── survival.py               # Survival analysis basics (Kaplan-Meier, Cox models, etc.)
├── examples/                     # Real-world case studies & applications
│   ├── RKZ_Regulierungsstatistik/      # Hierarchical KPI scoring & regulatory statistics
│   ├── Cross_Selling_BamS/             # ML-driven cross-selling prediction
│   ├── Hypothesis_Testing/             # A/B testing and classical hypothesis tests
│   ├── Weekend_Users_Hypo_Test/        # User behavior hypothesis testing
│   └── Weighted_Temperature/           # Weighted statistical modeling
├── notebooks/
│   ├── README.md
│   ├── 01_test_src_package.ipynb       # Validation of src/ modules
│   └── 02_real_world_examples.ipynb    # End-to-end demonstrations
├── Automation_monthly_run/       # Scheduled automation & reporting scripts
├── README.md
├── requirements.txt
├── LICENSE
└── .gitignore

About

This project provides clean, well-tested, and reusable Python implementations of key statistical inference methods used in modern data analysis and machine learning. The focus is on both classical frequentist approaches and modern shrinkage/regularization techniques that improve robustness in high-dimensional or small-sample settings.

Methods are implemented from scratch (or with minimal dependencies) to promote understanding, while also demonstrating practical usage with statsmodels, scikit-learn, and pycaret.

Installation

git clone https://github.com/Shahabed/Statistical-Inference.git
cd Statistical-Inference
pip install -r requirements.txt

Core dependencies (see requirements.txt):

• numpy, pandas, matplotlib, seaborn
• scipy, statsmodels
• scikit-learn, pycaret (optional for examples)

Usage

Using the Core Modules (src/)

Each module in src/ can be imported directly:

from src.bootstrap import bootstrap_ci
from src.hypothesis_testing import t_test, multiple_testing_correction
from src.empirical_bayes import james_stein_estimator
from src.lasso import lasso_path
# etc.

Example: Bootstrap Confidence Interval

import numpy as np
from src.bootstrap import bootstrap_ci

data = np.random.normal(0, 1, 1000)
ci_lower, ci_upper = bootstrap_ci(data, np.mean, n_boot=10000)
print(f"95% CI for mean: [{ci_lower:.3f}, {ci_upper:.3f}]")

See individual module docstrings and the notebooks for full examples and parameter details.

Running Notebooks

jupyter notebook notebooks/

• 01_test_src_package.ipynb — Unit tests / validation of the core implementations
• 02_real_world_examples.ipynb — Complete pipelines on real datasets

Real-World Examples

Explore the examples/ folder for production-style case studies:

• Regulatory statistics and hierarchical modeling
• Cross-selling prediction with machine learning
• Classic and modern hypothesis testing scenarios
• Weighted statistical models

Key Methods Implemented

Module	Techniques Covered	Typical Use Case
bootstrap.py	Non-parametric bootstrap, CI, bias correction	Small samples, complex statistics
hypothesis_testing.py	t-tests, chi-square, permutation tests, FDR	A/B testing, group comparisons
empirical_bayes.py	James-Stein estimator, shrinkage	High-dimensional means estimation
shrinkage.py	Ridge, general shrinkage estimators	Multicollinear or noisy data
lasso.py	LASSO, regularization path, cross-validation	Feature selection, sparse models
survival.py	Kaplan-Meier, Nelson-Aalen, basic Cox	Time-to-event analysis

Why This Repository?

Many statistical libraries exist, but this project emphasizes:

• Transparency: Code is readable and commented.
• Educational value: Good for learning how the methods work under the hood.
• Practicality: Ready-to-use functions with sensible defaults.
• Real data: Examples drawn from actual business/regulatory/ scientific problems.

Contributing

Contributions are welcome! Please:

1. Fork the repo
2. Create a feature branch
3. Add tests for new functionality
4. Submit a pull request

For major changes, open an issue first to discuss.

Acknowledgments

• Inspired by classic statistical literature (Efron, Hastie, Tibshirani, etc.)
• Built on top of excellent scientific Python ecosystem (numpy, scipy, statsmodels, scikit-learn)
• Real-world examples contributed from various data science projects

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