Monte Carlo sampling is a fundamental aspect of Monte Carlo methods, involving the generation of random samples to approximate numerical results. The term “Monte Carlo” itself implies a reliance on randomness, and sampling is at the core of these methods. Here are the key aspects of Monte Carlo sampling:
1. Random Sampling:
- Monte Carlo sampling involves drawing random samples from a specified probability distribution. The goal is to simulate the behavior of a system or estimate numerical quantities.
- Random samples are drawn from a specified probability distribution, determining the likelihood of different outcomes.
- In practice, random numbers are often generated using algorithms called pseudo-random number generators, providing sequences that appear random but are deterministic and reproducible.
- Random sampling is not limited to Monte Carlo methods and is widely used in various fields, including statistics, machine learning, and experimental design.
- The reliability of random sampling is grounded in the Law of Large Numbers, which states that as the number of samples increases, the sample average converges to the expected value.
- The introduction of randomness through sampling is…
