The Unreasonable Effectiveness of Quasirandom Sequences

I present a new low discrepancy quasirandom sequence that offers many substantial improvements over other popular sequences such as the Sobol and Halton sequences.

Figure 1a. Comparison of the various low discrepancy quasirandom sequences. Note that the newly proposed $R$-sequence produces more evenly spaced points than any of the other methods. Furthermore, all other current methods require careful selection of basis parameters, and if not chosen carefully can lead to degeneracy (eg top right).

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A probabilistic approach
to fractional factorial design

I describe a probabilistic alternative to fractional factorial design based on the Sobol’ low discrepancy quasirandom sequence. This method is robust to aliasing¬† (confounders), is often simpler to implement than traditional fractional factorial sample designs, and produces more accurate results than simple random sampling.

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to fractional factorial design”