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Monte Carlo Simulation

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Monte Carlo Integration

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A technique for estimating the value of an integral using random sampling.

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Antithetic Variates

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A variance reduction technique that involves using negatively correlated variables to decrease the variance of the simulation.

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Law of Large Numbers

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A principle that states that as a sample size grows, its mean gets closer to the average of the whole population.

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Variance Reduction Techniques

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Methods employed in Monte Carlo simulations to decrease the variance of the simulation results without increasing the number of samples.

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Control Variates

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A variance reduction technique that improves estimation precision by exploiting the correlation between the variable of interest and a control variable with a known expected value.

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Random Sampling

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The process of generating random variables from a known probability distribution to simulate diverse outcomes in a system.

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Convergence

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The process by which Monte Carlo simulation results become closer to the true value as more iterations are performed.

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Probability Distribution

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A mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Importance Sampling

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A variance reduction technique that involves changing the probability distribution to draw samples from areas where the integrand is large.

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Bootstrap Method

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A resampling technique used to estimate statistics on a population by sampling a dataset with replacement.

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