winning entry at MCqMC’16

mcqmc4The nice logo of MCqMC 2016 was a collection of eight series of QMC dots on the unit (?) cube. The organisers set a competition to identify the principles behind those quasi-random sets and as I had no idea for most of them I entered very random sets unconnected with algorithmia, for which I got an honourable mention and a CD prize (if not the conference staff tee-shirt I was coveting!) Art Owen sent me back my entry, posted below and hopefully (or not!) readable.dots

5 Responses to “winning entry at MCqMC’16”

  1. I’m back from vacation. The 8 constructions are:

    random grid Halton points Fibonacci lattice
    digital net scrambled net sparse grid blue noise

    Synonyms were accepted.

    The random points come from the Mersenne Twister. Nobody guessed the seed.

    The Halton points use, as usual, bases 2 and 3.

    The digital net is done in base 3. It is also a Hammersley point set.

    The scrambled net used a nested uniform scramble. Wei-Liem Loh has shown that this scramble yields a CLT under reasonable conditions. No other scramble is known to do so.

    For sparse grid, we would have accepted ‘Smolyak points’.

    For blue noise, we would have accepted ‘Poisson disk’ or ‘hard disk’. They are used in graphical rendering where spectral properties of the points are important and where you don’t want any pair of points to be too close to each other. (Read up on work by Alex Keller and/or Eugene Fiume, among others, to see more.)

    Three important omitted constructions:
    – Sobol’ points (his 90th birthday was day one of the conference)
    – higher order digital net (due to Josef Dick and co-authors)
    – polynomial lattice rules (like the ones Dirk Nuyens showed, not the older constructions that may qualify by being special cses)

    The upper left corner also illustrates MCMC as it is commonly done using IID inputs, though some advantages can be attained by substituting completely uniformly distributed points.

  2. That entry made it fun to be the MCQMC emcee.

    The serious winning entry was from Adrian Ebert (KU Leuven) and another humourous one came from Pieterjan Robbe (KU Leuven).

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