Statistics

This repository contains notes, explanations, and code snippets related to essential statistics concepts and techniques. The materials cover a range of topics, from basic probability and descriptive statistics to more advanced concepts like hypothesis testing and confidence intervals.

Requirements

The programming examples in this repository are primarily implemented in Python due to its simplicity, versatility, and the robustness of its scientific computing ecosystem. The code exploits various widely-used libraries such as NumPy for numerical computing, SciPy for advanced scientific computations, and pandas for data manipulation and analysis. As a result, a basic understanding of Python programming and its scientific libraries would be beneficial for comprehending and utilizing the code snippets.

To ensure you can run the code snippets and notebooks seamlessly, please make sure your environment fulfills the Python dependencies. We recommend setting up a virtual environment to avoid any package conflicts.

You can set up a virtual environment using the following steps:

# Create a virtual environment
python3 -m venv env

To activate the virtual environment, the command differs based on your operating system:

# On Windows, use:
env\Scripts\activate

# On Unix or MacOS, use:
source env/bin/activate

Once the virtual environment is activated, install the necessary packages using pip:

pip install -r requirements.txt

Now, you should be ready to run the code in this repository.

# Here's an example of how you can run a Python script
python scripts/basic_concepts/basic_concepts.py

Remember to replace 'scripts/basic_concepts/basic_concepts.py' with the actual name of the script you wish to run.

When you're done working, you can deactivate the virtual environment by simply running the deactivate command.

deactivate

Topics

Basic Concepts

Concept	Notes	Implementation	Examples
Introduction to Statistics
Descriptive Statistics
Introduction to Probability		N/A	N/A
Geometric Probability
Axioms of Probability		N/A	N/A
Conditional Probability and Independence		N/A	N/A
Bayes Theorem
Probability Trees		N/A	N/A
Total Probability		N/A	N/A
Bayesian vs Frequentist

Probability Distributions

Concept	Notes	Implementation	Examples
Introduction to Distributions
Central Limit Theorem
Beta Distribution
Chi-Square Distribution
Exponential Distribution
F Distribution
Gamma Distribution
Log-Normal Distribution
Normal Distribution
Student t Distribution
Uniform Distribution
Binomial Distribution
Geometric Distribution
Negative Binomial Distribution
Poisson Distribution

Hypothesis Testing and Confidence Intervals

Concept	Notes	Implementation	Examples
Null Hypothesis
Hypothesis Testing
Type I and Type II Errors
Confidence Intervals
Multiple Comparisons
Analysis of Variance (ANOVA)
Analysis of Categorical Data
Resampling

Correlation and Regression

Concept	Notes	Implementation	Examples
Correlation
Covariance
Simple Linear Regression
Multiple Regression
Logistic Regression
Metrics

Time Series Analysis

Concept	Notes	Implementation	Examples
Time Series
Seasonality and Trends
Series
Difference Equations
Stationarity
Invertibility
Backward Shift Operator
Random Walk
Forecasting
Autoregressive Models
Moving Average Models
Autocorrelation Function
Autocovariance Function
Yule-Walker Equations

Spatial Statistics

Concept	Notes	Implementation	Examples
Point Processes
Spatial Autocorrelation
Geostatistics

How to Contribute

We encourage contributions that enhance the repository's value. To contribute:

1. Fork the repository.
2. Create your feature branch (git checkout -b feature/AmazingFeature).
3. Commit your changes (git commit -m 'Add some AmazingFeature').
4. Push to the branch (git push origin feature/AmazingFeature).
5. Open a Pull Request.

References

Online Courses and Educational Platforms

• Harvard University's Introduction to Probability
• edX: Fundamentals of Statistics

Books and eBooks

• Think Bayes by Allen Downey
• SpringerLink: An Introduction to Statistical Learning
• SpringerLink: The Elements of Statistical Learning

Resources and Cheat Sheets

• Probability Cheatsheet on GitHub
• Allen Downey's Blog on Probability and Bayesian Stats
• Saylor Academy: Introductory Statistics
• Statistical Learning with Sparsity by Hastie, Tibshirani, and Wainwright
• Statistics How To: Probability and Statistics Main Index

Video Lectures and Playlists

• Oxford Playlist on Probability and Statistics

License

This project is licensed under the MIT License - see the LICENSE file for details.