2,810 research outputs found
A rule of thumb for riffle shuffling
We study how many riffle shuffles are required to mix n cards if only certain
features of the deck are of interest, e.g. suits disregarded or only the colors
of interest. For these features, the number of shuffles drops from 3/2 log_2(n)
to log_2(n). We derive closed formulae and an asymptotic `rule of thumb'
formula which is remarkably accurate.Comment: 27 pages, 5 table
Randomised algorithms for counting and generating combinatorial structures
SIGLEAvailable from British Library Document Supply Centre- DSC:D85048 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Sequential Quasi-Monte Carlo
We derive and study SQMC (Sequential Quasi-Monte Carlo), a class of
algorithms obtained by introducing QMC point sets in particle filtering. SQMC
is related to, and may be seen as an extension of, the array-RQMC algorithm of
L'Ecuyer et al. (2006). The complexity of SQMC is , where is
the number of simulations at each iteration, and its error rate is smaller than
the Monte Carlo rate . The only requirement to implement SQMC is
the ability to write the simulation of particle given as a
deterministic function of and a fixed number of uniform variates.
We show that SQMC is amenable to the same extensions as standard SMC, such as
forward smoothing, backward smoothing, unbiased likelihood evaluation, and so
on. In particular, SQMC may replace SMC within a PMCMC (particle Markov chain
Monte Carlo) algorithm. We establish several convergence results. We provide
numerical evidence that SQMC may significantly outperform SMC in practical
scenarios.Comment: 55 pages, 10 figures (final version
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