Statistical Computing

This repository contains assignments and projects for the Statistical Computing course in the Master's program at CIMAT (Center for Research in Mathematics). The coursework emphasizes the practical application of statistical theory using computational methods, primarily with R programming.

📚 Course Content

This course covers key areas of statistical computing including:

1. Generalized linear models
   • Logistic and Poisson regression models
   • Generalized linear models, the general case
   • Linear models of variance and covariance analysis
   • Log-linear models
2. Time series analysis
   • Stochastic processes
   • Autocovariance and autocorrelation
   • Stationary time series
   • Autoregressive processes
   • Moving average processes
   • ARMA processes
   • Spectral analysis of time series
3. Computational intensive estimation methods
   • EM algorithm
   • MCMC algorithms
   • Bootstrap
4. Model evaluation and selection in regression analysis
   • Criteria for evaluating and selecting the appropriate model
   • Prediction error estimation: Cross-validation
   • Model selection methods: Stepwise methods, AIC, BIC
   • Variable selection methods: Regularization, Ridge, LARS, LASSO
5. Data imputation methods
   • Methods based on regression and covariance analysis.
   • Methods based on the EM algorithm
   • Bayesian imputation
   • Methods based on machine learning techniques

📁 Repository Structure

The repository follows the next structure:

statistical-computing/
├── homework/
│   ├── 01_poisson_logistic_regression/
│   │   ├── R/
│   │   │   ├── data/
│   │   │   ├── results/
│   │   │   └── scripts/
│   │   ├── report/
│   │   ├── README.md
│   │   └── setup_renv.R
│   └── 02_glms_categorical_and_count_data/
│   │   ├── R/
│   │   │   ├── data/
│   │   │   ├── results/
│   │   │   └── scripts/
│   │   ├── report/
│   │   ├── README.md
│   │   └── setup_renv.R
├── LICENSE
└── README.md

📊 Assignments

The current course progress:

Assignment	Topic	Key Methods	Link
01	Poisson & Logistic Regression	GLMs, MLE, McNemar's Test	📂 View
02	GLMs: Categorical & Count Data	Logistic models, Poisson regression, diagnostics	📂 View
03	...	...	...
04	...	...	...

🛠 Technical Stack

Programming & Analysis:

• R (≥4.3.0): Statistical computing and graphics
• Key R Packages: dplyr, ggplot2, MASS

Documentation & Reporting:

• LaTeX: Professional mathematical typesetting
• Markdown: Repository documentation
• Git: Version control

Development Tools:

• RStudio: Integrated development environment
• renv: Reproducible package management

🚀 Getting Started

Prerequisites

Ensure you have the following installed:

• R (version ≥4.3.0)
• RStudio (recommended)
• LaTeX distribution (TeX Live, MiKTeX, or MacTeX)
• Git

📄 License

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

---

This repository represents academic work in statistical computing, demonstrating the integration of mathematical theory with practical data analysis using modern computational tools.