Monte Carlo methods are a broad class of computational algorithms that utilize repeated random sampling to obtain numerical results. The fundamental idea behind these methods is to inject randomness into a system to effectively solve complex mathematical problems. They are particularly useful in scenarios where deterministic solutions are difficult to achieve, such as in optimization and the evaluation of complex probabilities and functions ²⁴.

There are three main classes of Monte Carlo sampling: direct sampling, importance sampling, and rejection sampling. Direct sampling involves sampling from a distribution without prior information, while importance sampling focuses on sampling from a distribution that emphasizes certain areas to improve efficiency. Rejection sampling is a technique that samples from a target distribution by accepting or rejecting samples based on a criterion ².

Monte Carlo methods are widely applicable, including in fields like finance, physics, and engineering, where they can be used to model uncertainty and simulate various scenarios ³⁵.