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Monte Carlo Simulation
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Random Sampling
The process of generating random variables from a known probability distribution to simulate diverse outcomes in a system.
Convergence
The process by which Monte Carlo simulation results become closer to the true value as more iterations are performed.
Law of Large Numbers
A principle that states that as a sample size grows, its mean gets closer to the average of the whole population.
Monte Carlo Integration
A technique for estimating the value of an integral using random sampling.
Control Variates
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.
Variance Reduction Techniques
Methods employed in Monte Carlo simulations to decrease the variance of the simulation results without increasing the number of samples.
Antithetic Variates
A variance reduction technique that involves using negatively correlated variables to decrease the variance of the simulation.
Probability Distribution
A mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
Bootstrap Method
A resampling technique used to estimate statistics on a population by sampling a dataset with replacement.
Importance Sampling
A variance reduction technique that involves changing the probability distribution to draw samples from areas where the integrand is large.
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