The article provides a refinement for the volume-corrected Laplace-Metropolis estimator of the marginal likelihood of DiCiccio et al. The correction volume of probability a in DiCiccio et al. is fixed and suggested to take the value alpha = 0.05. In this article a is selected based on an asymptotic analysis to minimize the mean square relative error (MSRE). This optimal choice of a is shown to be invariant under linear transformations. The invariance property leads to easy implementation for multivariate problems. An implementation procedure is provided for practical use. A simulation study and a real data example are presented.
