Control variates, the Glossary

Table of Contents

1. 13 relations: Antithetic variates, Bias of an estimator, Continuous uniform distribution, Expected value, Importance sampling, Least squares, Linear regression, Monte Carlo integration, Monte Carlo method, Pearson correlation coefficient, Statistic, Variance, Variance reduction.

2. Statistical randomness
3. Variance reduction

Antithetic variates

In statistics, the antithetic variates method is a variance reduction technique used in Monte Carlo methods. Control variates and antithetic variates are computational statistics, Monte Carlo methods and variance reduction.

See Control variates and Antithetic variates

Bias of an estimator

In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated.

See Control variates and Bias of an estimator

Continuous uniform distribution

In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions.

See Control variates and Continuous uniform distribution

Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

See Control variates and Expected value

Importance sampling

Importance sampling is a Monte Carlo method for evaluating properties of a particular distribution, while only having samples generated from a different distribution than the distribution of interest. Control variates and Importance sampling are Monte Carlo methods and variance reduction.

See Control variates and Importance sampling

Least squares

The method of least squares is a parameter estimation method in regression analysis based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation.

See Control variates and Least squares

Linear regression

In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables).

See Control variates and Linear regression

Monte Carlo integration

In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers. Control variates and Monte Carlo integration are Monte Carlo methods.

See Control variates and Monte Carlo integration

Monte Carlo method

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. Control variates and Monte Carlo method are Monte Carlo methods.

See Control variates and Monte Carlo method

Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data.

See Control variates and Pearson correlation coefficient

Statistic

A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose.

See Control variates and Statistic

Variance

In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.

See Control variates and Variance

Variance reduction

In mathematics, more specifically in the theory of Monte Carlo methods, variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. Control variates and variance reduction are computational statistics and Monte Carlo methods.

See Control variates and Variance reduction

See also

Statistical randomness

• Accuracy and precision
• Algebra of random variables
• Alignments of random points
• Clustering illusion
• Complete spatial randomness
• Concentration dimension
• Control variates
• Differential entropy
• Entropy (information theory)
• Entropy estimation
• Exchangeable random variables
• Gaussian process emulator
• Index of dispersion
• Infinite monkey theorem
• Information fluctuation complexity
• Low-discrepancy sequences
• Martingale theory
• Median trick
• Monte Carlo methods
• Poisson random measure
• Proofs of convergence of random variables
• Pseudorandomness
• Random binary tree
• Random compact set
• Random element
• Random matrices
• Random number generation
• Random sequence
• Random variable
• Random variate
• Randomized algorithms
• Randomness
• Randomness test
• Seven states of randomness
• Statistical fluctuations
• Statistical randomness
• Stochastic computing
• Stochastic processes

Variance reduction

• Antithetic variates
• Control variates
• Importance sampling
• Line sampling
• Stratified sampling
• Subset simulation
• VEGAS algorithm
• Variance reduction

References

[1] https://en.wikipedia.org/wiki/Control_variates

Also known as Control variate, Regression sampling.