Part II: Simulation-Based Methods

This part covers simulation-based methods including Monte Carlo techniques, random variable generation, parametric inference, linear models, and resampling methods. We develop both the mathematical theory behind these methods and their practical implementation in Python.

Topics covered: Monte Carlo fundamentals and convergence; inverse CDF method and Box-Muller transformation; rejection sampling and variance reduction; exponential families and maximum likelihood; linear models and generalized linear models; jackknife, bootstrap, and cross-validation; parametric bootstrap and bias correction; confidence interval construction and model selection.

Chapters

• 1. Chapter 2: Monte Carlo Simulation
  • 1.1. Monte Carlo Fundamentals
  • 1.2. Uniform Random Variates
  • 1.3. Inverse CDF Method
• 2. Chapter 3: Frequentist Statistical Inference
  • 2.1. Sampling Variability
  • 2.2. Statistical Estimators
  • 2.3. Plugin Methods
  • 2.4. Parametric Inference
  • 2.5. Exponential Families
  • 2.6. Maximum Likelihood
  • 2.7. Linear Models
  • 2.8. Generalized Linear Models
• 3. Chapter 4: Resampling Methods
  • 3.1. Jackknife Introduction
  • 3.2. Bootstrap Fundamentals
  • 3.3. Nonparametric Bootstrap
  • 3.4. Parametric Bootstrap
  • 3.5. Confidence Intervals
  • 3.6. Bias Correction
  • 3.7. Cross Validation Loo
  • 3.8. Cross Validation K Fold
  • 3.9. Model Selection