Randomized Quasi-Monte Carlo and Its Applications




Sorensen, Curtis Dane

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This paper shows, through example and analysis, that applying randomized quasi-Monte Carlo (RQMC) into approximate Bayesian computation (ABC) and Bayesian generative adversarial network (GAN) in place of simple Monte Carlo methods does indeed yield improvements in accuracy, speed, and variety of images produced. To mitigate the drawbacks of simple Monte Carlo and quasi-Monte Carlo methods of parameter estimation while still retaining their advantages, researchers introduced randomized quasi-Monte Carlo (RQMC) methods in the last decade. Randomized quasi-Monte Carlo methods construct a family of low discrepancy sequences, from which one can draw a sequence at random and use it to obtain an estimate for the integral. Hence, statistical analysis can be applied to multiple estimates obtained this way in order to measure estimation error. This paper further advocates and demonstrates the specific application of RQMC in both ABC and GAN in situations where simple Monte Carlo methods are currently used. Original analysis and results within this paper show that incorporating the RQMC does yield improvements. This relatively minor change in the algorithms allows improvements in the accuracy of estimated values and, in some cases, in speed as well. The potential for applying RQMC in this new way is broad and exciting. Because ABC and GAN are used in multiple fields, this innovation has the potential to influence a wide variety of research areas. Future research is also merited to determine the impact of RQMC in settings beyond ABC and GAN. The application of RQMC in these additional settings can then be similarly evaluated for improvements in accuracy and speed, making this application a valuable tool for scholars and professionals.


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Approximate Bayesian Computation, generative adversarial network, Randomized quasi-Monte Carlo



Management Science and Statistics