Monte Carlo Basics

Topics:

• Challenges to analytical integration
• Pros and cons of MC techniques
• History of MC and random sampling
• Numerical quadrature in one dimension
• Tensor product quadrature rules in higher dimensions
• Convergence rate of quadrature and the curse of dimensionality
• Discontinuous integrands
• Probability density functions
• Expected values and variance
• Monte Carlo estimators
• Convergence of Monte Carlo
• Unbiased vs. biased estimators