Grid-based exploration of cosmological parameter space with Snake
  We present a fully parallelized grid-based parameter estimation algorithm for
investigating multidimensional likelihoods called Snake, and apply it to
cosmological parameter estimation. The basic idea is to map out the likelihood
grid-cell by grid-cell according to decreasing likelihood, and stop when a
certain threshold has been reached. This approach improves vastly on the "curse
of dimensionality" problem plaguing standard grid-based parameter estimation
simply by disregarding grid-cells with negligible likelihood. The main
advantages of this method compared to standard Metropolis-Hastings MCMC methods
include 1) trivial extraction of arbitrary conditional distributions; 2) direct
access to Bayesian evidences; 3) better sampling of the tails of the
distribution; and 4) nearly perfect parallelization scaling. The main
disadvantage is, as in the case of brute-force grid-based evaluation, a
dependency on the number of parameters, N_par. One of the main goals of the
present paper is to determine how large N_par can be, while still maintaining
reasonable computational efficiency; we find that N_par = 12$ is well within
the capabilities of the method. The performance of the code is tested by
comparing cosmological parameters estimated using Snake and the WMAP-7 data
with those obtained using CosmoMC, the current standard code in the field. We
find fully consistent results, with similar computational expenses, but shorter
wall time due to the perfect parallelization scheme.
