Monte Carlo Integration
Monte Carlo Integration is a numerical technique for approximating definite integrals using random sampling and statistical methods. It is particularly useful for high-dimensional integrals or complex domains where traditional deterministic methods (like quadrature) become inefficient or intractable. The method relies on the law of large numbers to estimate the integral by averaging function values at randomly chosen points.
Developers should learn Monte Carlo Integration when dealing with problems in computational physics, finance (e.g., option pricing), computer graphics (e.g., rendering), or machine learning (e.g., Bayesian inference), where integrals are multi-dimensional or have irregular boundaries. It is essential for simulations and probabilistic models where analytical solutions are unavailable, offering a flexible and often simpler approach compared to deterministic numerical integration.