Exploring quasi Monte Carlo for marginal density approximation

We first review quasi Monte Carlo (QMC) integration for approximating integrals, which we believe is a useful tool often overlooked by statistics researchers. We then present a manually-adaptive extension of QMC for approximating marginal densities when the joint density is known up to a normalization constant. Randomization and a batch-wise approach involving (0,s)-sequences are the cornerstones of our method. By incorporating a variety of graphical diagnostics the method allows the user to adaptively allocate points for joint density function evaluations. Through intelligent allocation of resources to different regions of the marginal space, the method can quickly produce reliable marginal density approximations in moderate dimensions. We demonstrate by examples that adaptive QMC can be a viable alternative to the Metropolis algorithm.