This paper contributes to portfolio selection methodology using bayesian theory. A new estimation approach is applied to forecast the mean vector and covariance matrix of returns. The proposed method accounts for estimation errors. We compare the performance of traditional Mean Variance optimization of Markowitz with Michaudís Resampled Efficiency approach in a comprehensive simulation study for bayesian estimator and Implicit estimator. We carried out a numerical optimization procedure to maximize the expected utility using the MCMC samples from the posterior and the predictive distribution.