Optimal antithetic sampling plans

Roach, William; Wright, Roger L.

doi:10.1080/00949657708810144

Cited by 9 publications

(5 citation statements)

References 15 publications

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“…These transformations preserve uniformity and provide a general framework to the construction of antithetic vectors. The use of transformations to span the set of antithetic vectors was pioneered by Andréasson (1972) and Andréasson and Dahlquist (1972) and discussed further by Roach and Wright (1977). First, we define deterministic compositions and present reflections as a particular case.…”

Section: Antithetic Vector Transformationsmentioning

confidence: 99%

“…This led earlier researchers to propose feasible, yet sub-optimal sampling solutions, including Hammersley and Morton's (Hammersley and Morton, 1956) proposal for d > 2. Andréasson (1972), Andréasson and Dahlquist (1972) and Roach and Wright (1977) follow a group theoretic approach. In particular, Roach and Wright (1977), build on Andréasson (1972), Andréasson and Dahlquist (1972) and Tukey (1957), draws a parallel with systematic sampling.…”

Section: Introductionmentioning

confidence: 99%

“…Andréasson (1972), Andréasson and Dahlquist (1972) and Roach and Wright (1977) follow a group theoretic approach. In particular, Roach and Wright (1977), build on Andréasson (1972), Andréasson and Dahlquist (1972) and Tukey (1957), draws a parallel with systematic sampling. Its solutions for d = 2, in the case of non-monotonic f s, relies on discretization, optimal transport and a branch and bound algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Living on the Edge: An Unified Approach to Antithetic Sampling

Casarin¹,

Craiu²,

Frattarolo³

et al. 2021

Preprint

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We identify recurrent ingredients in the antithetic sampling literature leading to a unified sampling framework. We introduce a new class of antithetic schemes that includes the most used antithetic proposals. This perspective enables the derivation of new properties of the sampling schemes: i) optimality in the Kullback-Leibler sense; ii) closed-form multivariate Kendall's τ and Spearman's ρ; iii)ranking in concordance order and iv) a central limit theorem that characterizes stochastic behavior of Monte Carlo estimators when the sample size tends to infinity. Finally, we provide applications to Monte Carlo integration and Markov Chain Monte Carlo Bayesian estimation.

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Section: Antithetic Vector Transformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Living on the Edge: An Unified Approach to Antithetic Sampling

Casarin¹,

Craiu²,

Frattarolo³

et al. 2021

Preprint

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show abstract

“…With these transformations, the joint distribution of the pair (V 1 , v 2 ) is Roach and Wright (1977) sought optimal antithetic sampling plans for the estimator t = ~(V 1 + v 2 ). As in Case I, minimizing Var(t) is equivalent to minimizing Cov(V 1 , v 2 ); this in turn is equivalent to minimizing E(V 1 ·v 2 ).…”

Section: Summary and Applicationsmentioning

confidence: 99%

Antithetic Sampling with Multivariate Inputs

Wilson

1983

American Journal of Mathematical and Management Sciences

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“…The linear program above can be classified as a bottleneck transportation problem with a side constraint (BTPSC), where the side constraint is constraint (5). This approach to representing probability assignment problems as transportation problems was used by Roach and Wright (1977) to find optimal antithetic sampling plans. Evans (1984) has shown that the Northwest Corner Rule (NWCR) can be used to find an optimal solution to the following transportation problem: Minimize…”

Section: O P T I M a L C H A R A C T E R I Z A T I O N S Of Bivari-atmentioning

confidence: 99%

Characterizing distributions of discrete bivariate random variables for simulation and evaluation of solution methods

Moore¹,

Peterson²,

Reilly³

1990 Winter Simulation Conference Proceedings

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Results are presented from empirical evaluations of the performance of solution procedures on random binary knapsack and weighted set covering problems in which correlation is induced between the objective function and constraint coefficients. It is concluded that the performance of the solution procedures degrades as the correlation induced among the test problem parameters is increased and that test problems with structured dependence should be used for many empirical evaluations of solution methods.Since structured dependence in discrete optimization test problems is desirable, ways t o characterize the joint distribution of a discrete bivariate random variable for any feasible correlation are needed. The problem of finding a characterization with the maximum value of the smallest probability for any possible point is formulated as a linear program. An efficient algorithm based on the Northwest Corner Rule and a simple probability reallocation scheme is presented and demonstrated on a small example.

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Optimal antithetic sampling plans

Cited by 9 publications

References 15 publications

Living on the Edge: An Unified Approach to Antithetic Sampling

Living on the Edge: An Unified Approach to Antithetic Sampling

Antithetic Sampling with Multivariate Inputs

Characterizing distributions of discrete bivariate random variables for simulation and evaluation of solution methods

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