An Adaptive Quasi Monte Carlo Alternative to Metropolis

We present a manually-adaptive extension of Quasi Monte Carlo (QMC) integration for approximating marginal densities, moments, and quantiles 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 the technique. By incorporating a variety of graphical diagnostics the method allows the user to adap-tively allocate points for joint density function evaluations. Through intelligent allocation of resources to diierent 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.