🤖 AI Summary
This study addresses the limitations of independent and identically distributed (iid) sampling in achieving adequate space-filling and coverage properties for multivariate distribution simulation. We extend quantile stratified sampling to multivariate normal and other multivariate distributions by introducing an ordered log-density evaluation mechanism, which effectively mitigates sample clustering in high-dimensional spaces. Experimental results demonstrate that the proposed method significantly outperforms traditional iid sampling in terms of spatial uniformity and coverage completeness. Consequently, this approach provides a more representative sampling strategy for efficient simulation of complex multivariate distributions, thereby enhancing the reliability of downstream statistical inference.
📝 Abstract
In this paper we show how to extend quantile-stratified sampling to produce simulations from various multivariate distributions. These simulations have desirable space-filling and coverage properties relative to simulation using IID sampling. We examine the coverage performance of these simulations against IID sampling by looking at plots of ordered log-density values from the simulations.