Randomized Halton Sequences

The Halton sequence is a well-known multi-dimensional low discrepancy sequence. In this paper, we propose a new method for randomizing the Halton sequence: we randomize the start point of each component of the sequence. This method combines the potential accuracy advantage of Halton sequence in multi-dimensional integration with the practical error estimation advantage of Monte Carlo methods. Theoretically, using multiple randomized Halton sequences as a variance reduction technique we can obtain an eeciency improvement over standard Monte Carlo under rather general conditions. Numerical results show that randomized Halton sequences have better performance than not only Monte Carlo, but also randomly shifted Halton sequences and (single long) purely deterministic skipped Halton sequence.