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Estimated MSEs of test functions at n ∈ {3125m, 1 ≤ m ≤ 40}, using the 4-dimensional Faure Sequence constructed in base 5, using factors [3, 2, 1, 4] (Faure 1992) and [3, 1, 4, 2] (Offset) and the Halton sequence with the corresponding permutations

Estimated MSEs of test functions at n ∈ {3125m, 1 ≤ m ≤ 40}, using the 4-dimensional Faure Sequence constructed in base 5, using factors [3, 2, 1, 4] (Faure 1992) and [3, 1, 4, 2] (Offset) and the Halton sequence with the corresponding permutations

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Figure 1: Estimated MSEs of test functions at n ∈ {3125m, 1 ≤ m ≤ 40},...
Figure 3:
Figure 4: Estimated MSEs test functions using the 4-, 12-and...
Figure 10: Comparing Random Linear Scrambling of the Halton sequence...
A negative dependence framework to assess different forms of scrambling
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  • Sep 2022
We use the framework of dependence to assess the benefits of scrambling randomly versus deterministically for Faure and Halton sequences. We attempt to answer the following questions: when a deterministic sequence has known defects for small sample sizes, should we address these defects by applying random scrambling or should we find a "good" deter...
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... is plotted on Figures 1 to 5 are the MSE for functions h 0 , h 1 , and g, and the variance for the SAN. In all cases the MSE or variance is estimated using V = 25 randomizations. ...

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