Minimal grid size for accurate posterior estimation with equidistant grids

Determine the minimal number of grid points required, as a function of model dimension and desired accuracy, for an equidistant precomputed grid over the parameter space to yield accurate posterior estimates when approximating E_{z|β}[S(z)] for Markov random field models with intractable normalizing constants.

Background

Equidistant grids over the parameter space are a long-standing and straightforward choice for precomputation in thermodynamic integration and related path-sampling methods. While easy to construct, such grids suffer from exponential growth in size with parameter dimension.

The paper highlights that, despite widespread use, there is no clear guidance on the minimal number of grid points needed to ensure accurate posterior estimates. Establishing this threshold would enable practitioners to balance computational cost against inferential accuracy in a principled manner.