This paper presents a novel approach to appraising the ensemble of models generated by Monte Carlo direct search methods, such as genetic algorithms and simulated annealing. The traditional approach often relies on only a small subset of the ensemble, or even a single model, for inference. The new method addresses the general case, where any ensemble of models can be used to guide a resampling of the parameter space. This resampled ensemble is then used to obtain measures of resolution and trade-off in the model parameters without solving the forward problem again. The algorithm is based on Voronoi cells and a Gibbs sampler, which allows for efficient parallel implementation. The computational costs and memory requirements are analyzed, showing that the method is highly scalable. The effectiveness of the resampling algorithm is demonstrated through a numerical example in receiver function inversion, where it is shown that useful constraints and error information can be derived from the ensemble.This paper presents a novel approach to appraising the ensemble of models generated by Monte Carlo direct search methods, such as genetic algorithms and simulated annealing. The traditional approach often relies on only a small subset of the ensemble, or even a single model, for inference. The new method addresses the general case, where any ensemble of models can be used to guide a resampling of the parameter space. This resampled ensemble is then used to obtain measures of resolution and trade-off in the model parameters without solving the forward problem again. The algorithm is based on Voronoi cells and a Gibbs sampler, which allows for efficient parallel implementation. The computational costs and memory requirements are analyzed, showing that the method is highly scalable. The effectiveness of the resampling algorithm is demonstrated through a numerical example in receiver function inversion, where it is shown that useful constraints and error information can be derived from the ensemble.