This paper presents a new approach to the appraisal of ensembles generated by direct search methods in geophysical inversion. The method uses the information in the ensemble to guide a resampling of the parameter space, allowing measures of resolution and trade-off in model parameters to be determined without further solving of the forward problem. The approach is based on a Bayesian framework and uses Voronoi cells to construct an approximate posterior probability density function (PPD) from the input ensemble. This approximate PPD is then used to generate a second ensemble for Monte Carlo integration, enabling the evaluation of Bayesian integrals such as resolution and trade-off measures. The method is highly parallel and can be distributed across multiple computers. It is applicable to a wide variety of situations, including error analysis using ensembles generated by genetic algorithms or other direct search methods. The paper illustrates the method on a highly non-linear waveform inversion problem, showing how computation time and memory requirements scale with the dimension of the parameter space and size of the ensemble. The method is efficient and avoids the computational inefficiency associated with the loss factor, which is a common issue in importance sampling methods. The resampling algorithm is demonstrated on a numerical example involving the inversion of receiver functions for crustal seismic structure, where it successfully recovers useful constraints and error information from the input ensemble. The results show that the method can effectively evaluate Bayesian integrals and provide meaningful insights into the information contained in the ensemble.This paper presents a new approach to the appraisal of ensembles generated by direct search methods in geophysical inversion. The method uses the information in the ensemble to guide a resampling of the parameter space, allowing measures of resolution and trade-off in model parameters to be determined without further solving of the forward problem. The approach is based on a Bayesian framework and uses Voronoi cells to construct an approximate posterior probability density function (PPD) from the input ensemble. This approximate PPD is then used to generate a second ensemble for Monte Carlo integration, enabling the evaluation of Bayesian integrals such as resolution and trade-off measures. The method is highly parallel and can be distributed across multiple computers. It is applicable to a wide variety of situations, including error analysis using ensembles generated by genetic algorithms or other direct search methods. The paper illustrates the method on a highly non-linear waveform inversion problem, showing how computation time and memory requirements scale with the dimension of the parameter space and size of the ensemble. The method is efficient and avoids the computational inefficiency associated with the loss factor, which is a common issue in importance sampling methods. The resampling algorithm is demonstrated on a numerical example involving the inversion of receiver functions for crustal seismic structure, where it successfully recovers useful constraints and error information from the input ensemble. The results show that the method can effectively evaluate Bayesian integrals and provide meaningful insights into the information contained in the ensemble.