Implicit samplers are algorithms for producing independent, weighted samples
from multi-variate probability distributions. These are often applied in
Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to
analyze two implicit samplers in the small noise regime. Our analysis suggests
a symmetrization of the algo- rithms that leads to improved (implicit) sampling
schemes at a rel- atively small additional cost. Computational experiments
confirm the theory and show that symmetrization is effective for small noise
sampling problems