Numerical integration
Integrals often arise as quantities of interest in statistical analysis. For example, posterior expectations and risk/loss functions.
Unfortunately, many integrals cannot be expressed using elementary functions, and therefore cannot be computed exactly. To address this issue, various approximations are used, many of which involve using a computer to produce the approximation. In many cases, these approximations can be made arbitrarily accurate by increasing the computational resources afforded.
We will cover some deterministic numerical integration algorithms as well as some Monte Carlo algorithms.