  In some cases, computational benefit can be gained by exploring the hyper
parameter space using a deterministic set of grid points instead of a Markov
chain. We view this as a numerical integration problem and make three unique
contributions. First, we explore the space using low discrepancy point sets
instead of a grid. This allows for accurate estimation of marginals of any
shape at a much lower computational cost than a grid based approach and thus
makes it possible to extend the computational benefit to a hyper parameter
space with higher dimensionality (10 or more). Second, we propose a new, quick
and easy method to estimate the marginal using a least squares polynomial and
prove the conditions under which this polynomial will converge to the true
marginal. Our results are valid for a wide range of point sets including grids,
random points and low discrepancy points. Third, we show that further accuracy
and efficiency can be gained by taking into consideration the functional
decomposition of the integrand and illustrate how this can be done using
anchored f-ANOVA on weighted spaces.
