The main computational problem in Bayesian Inference is computing the posterior distribution. More concretely, computing expectations of functions with respect to the posterior distributions. In this work we review some stochastic simulation methods for one-dimensional posterior distributions. We propose adapting these methods by using quasi-random numbers as a way to obtain better approximations to the target distribution and therefore an improvement in the estimations of posterior characteristics. We compare with the pseudo-random case. Finally, we illustrate by an example the extension to multidimensional problems.

keywords:  Bayesian Inference, Pseudo-random numbers, Quasi-random numbers, Simulation, F-discrepancy, Low-discrepancy point sets and sequences, Inverse transform method, Weighted Bootstrap, Ratio-of-uniform method.