Exploring quasi Monte Carlo for marginal density approximation

We ®rst 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 manuallyadaptive 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 di€erent 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.