Appendices

These appendices provide prerequisite review material and reference resources for the course. Students entering STAT 418 are expected to have foundational knowledge in probability, statistical inference, calculus, and numerical methods. The materials below offer a self-contained review of the key concepts that underpin the computational methods developed in the main chapters.

Prerequisites Review

• Appendix A: Calculus Review
  • From Formulas to Statistical Reasoning
  • Univariate Differentiation
  • Integration
  • Taylor Series and Approximation
  • Leibniz Rule and Differentiation Under the Integral
  • Multivariate Differential Calculus
  • Convexity and Optimization
  • Multivariate Taylor Expansion
  • Multiple Integrals and Change of Variables
  • Connections: From Calculus to Computation
  • Practice Problems
• Appendix B: Linear Algebra for Data Science
  • From Notation to Intuition
  • Vectors and Inner Products
  • Matrix Operations and Properties
  • Special Matrix Structures
  • Block Matrices
  • Column Space, Projections, and Least Squares
  • Matrix Decompositions
  • Quadratic Forms and Covariance
  • Matrix Calculus
  • Numerical Considerations
  • Key Takeaways
  • Looking Ahead
  • Practice Problems
• Appendix C: Numerical Analysis Review
  • From Exact to Approximate
  • Floating-Point Arithmetic
  • Root Finding
  • Numerical Optimization
  • Numerical Differentiation
  • Numerical Integration
  • Convergence and Stopping Criteria
  • Connections: From Numerical Analysis to Computation
  • Practice Problems
• Appendix D: Probability Distributions — Theory and Computation
  • From Abstract Foundations to Concrete Tools
  • The Python Ecosystem for Probability
  • Discrete Distributions
  • Continuous Distributions
  • Additional Important Distributions
  • Summary and Practical Guidelines
  • Conclusion
  • Practice Problems
• Appendix E: Statistical Inference Review
  • Point Estimation
  • Confidence Intervals
  • Hypothesis Testing
  • Sufficiency and Information
  • The Likelihood Function
  • Asymptotic Theory
  • Connections: From Review to Computation
  • Practice Problems
• Appendix F: Python Random Generation
  • From Mathematical Distributions to Computational Samples
  • The Python Ecosystem at a Glance
  • Understanding Pseudo-Random Number Generation
  • The Standard Library: random Module
  • NumPy: Fast Vectorized Random Sampling
  • SciPy Stats: The Complete Statistical Toolkit
  • Bringing It All Together: Library Selection Guide
  • Looking Ahead: From Random Numbers to Monte Carlo Methods
  • Practice Problem