Laplace approximations for posterior expectations when the mode occurs at the boundary of the parameter space

The Laplace method as an analytical tool for estimating expected values of functions of parameters and marginal densities in the Bayesian context is presented. Specifically, asymptotic expansions for posterior expectations of functions of parameters have been derived when the mode is on the edge of the parametric space. Second-order accuracy is obtained even if the mode is situated on the boundary.