Stochastic simulation
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
Simulation and the Monte Carlo Method
Simulation and the Monte Carlo Method
Time Series Analysis, Forecasting and Control
Time Series Analysis, Forecasting and Control
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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.