Unit 2962: Statistical Computing

1. Introduction to Statistical Computing

1.1 Overview of Statistical Computing

• Definition and scope of statistical computing
• Role of computation in modern statistics

1.2 Statistical Software Tools

• Review of popular software: R, Python, SAS, SPSS
• Advantages of open-source tools

1.3 Data Management

• Data types and structures
• Importing, cleaning, and organizing data

1.4 Data Visualization Basics

• Importance of visualization in statistics
• Basic plot types and their uses

1.5 Importance of Computational Tools

• Automation and reproducibility
• Enhancing accuracy and efficiency

2. Programming in R for Statistical Analysis

2.1 Introduction to R Programming Environment

• Installing and setting up R and RStudio
• R syntax and basic operations

2.2 Data Structures in R

• Vectors, matrices, lists, and data frames
• Indexing and subsetting data

2.3 Data Manipulation with R

• Using packages like dplyr and tidyr
• Filtering, summarizing, and transforming data

2.4 Basic Statistical Analysis in R

• Descriptive statistics (mean, median, variance)
• Hypothesis testing basics (t-tests, chi-square)
• Using R packages for statistical tests

2.5 Writing and Executing R Scripts

• Creating reproducible scripts
• Debugging and error handling

3. Data Visualization in Statistical Computing

3.1 Principles of Effective Visualization

• Clarity, accuracy, and aesthetics
• Choosing appropriate chart types

3.2 Creating Visualizations in R

• Base R plotting system
• ggplot2 grammar of graphics

3.3 Types of Plots and Graphs

• Histograms, bar charts, scatterplots, boxplots
• Advanced plots: heatmaps, density plots, time series

3.4 Enhancing Visualizations

• Adding labels, titles, legends
• Customizing themes and colors

3.5 Interactive Visualizations

• Introduction to shiny and plotly packages

4. Statistical Modeling and Simulation

4.1 Introduction to Statistical Models

• Concept of statistical modeling
• Types of models: linear, logistic, others

4.2 Building Statistical Models in R

• Fitting models using lm() and glm()
• Model diagnostics and interpretation

4.3 Simulation Techniques

• Generating random data
• Monte Carlo simulations

4.4 Model Evaluation and Validation

• Residual analysis
• Cross-validation techniques

4.5 Case Studies and Applications

• Practical examples of modeling and simulation

5. Advanced Topics in Statistical Computing

5.1 Machine Learning Algorithms

• Overview: supervised and unsupervised learning
• Implementing algorithms in R (e.g., random forests, k-means)

5.2 Big Data Processing

• Challenges of big data in statistics
• Using R with big data tools (e.g., data.table, sparklyr)

5.3 Parallel and High-Performance Computing

• Concepts of parallelism in computing
• Parallel processing in R (parallel, foreach packages)

5.4 Enhancing Statistical Analysis with Advanced Tools

• Integration with other languages (Python, C++)
• Automation and workflow management

5.5 Future Trends in Statistical Computing

• Emerging technologies and methodologies
• Ethical considerations and data privacy