What is Monte Carlo sampling?
Sources:
Monte Carlo sampling is a probabilistic technique used to approximate numerical results by generating random samples from a given probability distribution. Here are the key points based on experts' explanations:

Basic Concept:
 Monte Carlo sampling involves generating random numbers that follow a specified distribution. This can be done using a method called Markov Chain Monte Carlo (MCMC), which starts with an initial guess and produces a chain of samples through random perturbations. Each sample serves as a stepping stone for generating the next one 1.

Application:

Generating Random Numbers:
 Computers can generate random numbers using pseudorandom number generators, which employ complex formulas to ensure there are no discernible patterns. Alternatively, more "truly random" numbers can be generated based on physical processes such as temperature readings from a CPU 3.

Advantages and Challenges:

Practical Examples:
 For a simple random process, such as determining next moves in a game, Monte Carlo sampling can involve generating random numbers to decide based on predefined probabilities where each "turn" should go next 4.
Monte Carlo sampling is thus a powerful but computationally intensive method used across various fields like physics, finance, and machine learning to tackle problems involving complex probability distributions.
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