@inproceedings{710435fb535e4f62962cb471c4308f50,

title = "Discrepancy estimates for acceptance-rejection samplers using stratified inputs",

abstract = "In this paper we propose an acceptance-rejection sampler using stratified inputs as driver sequence. We estimate the discrepancy of the N-point set in (s −s)-dimensions generated by this algorithm. First we show an upper bound on the star-discrepancy of order N −d/2−1/(2s). Further we prove an upper bound on the qth moment of the L q-discrepancy (E[N q L qq,N]) 1/q for 2 ≤ q ≤ ∞, which is of order N ( 1−1/s)(1−1/q). The proposed approach is numerically tested and compared with the standard acceptance-rejection algorithm using pseudo-random inputs. We also present an improved convergence rate for a deterministic acceptance-rejection algorithm using (t, m, s)-nets as driver sequence. ",

keywords = "Monte Carlo method, Acceptance-rejection sampler, Discrepancy theory",

author = "Houying Zhu and Josef Dick",

year = "2016",

doi = "10.1007/978-3-319-33507-0_33",

language = "English",

isbn = "9783319335056",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer, Springer Nature",

pages = "599--619",

editor = "Ronald Cools and Dirk Nuyens",

booktitle = "Monte Carlo and Quasi-Monte Carlo Methods",

address = "United States",

note = "International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (11th : 2014) ; Conference date: 06-04-2014 Through 11-04-2014",

}