Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Scrambling sobol' and niederreiter-xing points
Journal of Complexity
Randomized Polynomial Lattice Rules for Multivariate Integration and Simulation
SIAM Journal on Scientific Computing
Variance Reduction via Lattice Rules
Management Science
Acceleration of the Multiple-Try Metropolis algorithm using antithetic and stratified sampling
Statistics and Computing
Coupling from the past with randomized quasi-Monte Carlo
Mathematics and Computers in Simulation
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In 1996, Propp and Wilson came up with a remarkably clever method for generating exact samples from the stationary distribution of a Markov chain [J.G. Propp, D.B. Wilson, Exact sampling with coupled Markov chains and applications to statistical mechanics, Random Structures and Algorithms 9 (1-2) (1996) 223-252]. Their method, called ''perfect sampling'' or ''exact sampling'' avoids the inherent bias of samples that are generated by running the chain for a large but fixed number of steps. It does so by using a strategy called ''coupling from the past''. Although the sampling mechanism used in their method is typically driven by independent random points, more structured sampling can also be used. Recently, Craiu and Meng [R.V. Craiu, X.-L. Meng, Antithetic coupling for perfect sampling, in: E.I. George (Ed.), Bayesian Methods with Applications to Science, Policy, and Official Statistics (Selected Papers from ISBA 2000), 2000, pp. 99-108; R.V. Craiu, X.-L. Meng, Multi-process parallel antithetic coupling for forward and backward Markov Chain Monte Carlo, Annals of Statistics 33 (2005) 661-697] suggested using different forms of antithetic coupling for that purpose. In this paper, we consider the use of highly uniform point sets to drive the exact sampling in Propp and Wilson's method, and illustrate the effectiveness of the proposed method with a few numerical examples.