Siddhartha Chib presents a method for computing the marginal likelihood of sample data given parameter draws from the posterior distribution in the context of Bayesian estimation using Gibbs sampling. The approach is applicable whether or not data augmentation is used. The marginal likelihood can be expressed as the product of the prior density and the likelihood function divided by the posterior density. An estimate of the posterior density is available if all complete conditional densities used in the Gibbs sampler have closed-form expressions. To improve accuracy, the posterior density is estimated at a high-density point, and the numerical standard error of the estimate is derived. The method is applied to probit regression and finite mixture models. The article includes a discussion of the numerical standard error and examples demonstrating the effectiveness of the method.Siddhartha Chib presents a method for computing the marginal likelihood of sample data given parameter draws from the posterior distribution in the context of Bayesian estimation using Gibbs sampling. The approach is applicable whether or not data augmentation is used. The marginal likelihood can be expressed as the product of the prior density and the likelihood function divided by the posterior density. An estimate of the posterior density is available if all complete conditional densities used in the Gibbs sampler have closed-form expressions. To improve accuracy, the posterior density is estimated at a high-density point, and the numerical standard error of the estimate is derived. The method is applied to probit regression and finite mixture models. The article includes a discussion of the numerical standard error and examples demonstrating the effectiveness of the method.