广义均匀比作为密度抽样的变换拒绝和广义逆的组合
On the Generalized Ratio of Uniforms as a Combination of Transformed Rejection and Extended Inverse of Density Sampling
摘要：
在这项工作中，我们研究了三个经典的抽样技术之间的关系：密度的倒数（欣钦定理），变换拒绝（TR）和广义均匀比（GRoU）。给出了一个单调的概率密度函数（PDF），证明了利用广义均匀比方法得到的变换面积可以等价地通过将变换后的拒绝抽样方法应用于目标密度的反函数而得到.然后，我们提供了一个扩展的经典逆密度的想法，表明它是完全等价的单调密度的GRoU方法。虽然我们专注于单调的概率密度函数（PDF），我们也讨论了如何在这里提出的结果可以扩展到任何非单调的PDF，可以分解成一个集合的区间，它是单调增加或减少。在这种一般情况下，我们显示与某些随机变量和广义逆PDF与GRoU技术的转换的连接。最后，我们还介绍了一个GRoU技术来处理无界目标密度。
英文摘要：
In this work we investigate the relationship among three classical sampling techniques: the inverse of density (Khintchine's theorem), the transformed rejection (TR) and the generalized ratio of uniforms (GRoU). Given a monotonic probability density function (PDF), we show that the transformed area obtained using the generalized ratio of uniforms method can be found equivalently by applying the transformed rejection sampling approach to the inverse function of the target density. Then we provide an extension of the classical inverse of density idea, showing that it is completely equivalent to the GRoU method for monotonic densities. Although we concentrate on monotonic probability density functions (PDFs), we also discuss how the results presented here can be extended to any non-monotonic PDF that can be decomposed into a collection of intervals where it is monotonically increasing or decreasing. In this general case, we show the connections with transformations of certain random variables and the generalized inverse PDF with the GRoU technique. Finally, we also introduce a GRoU technique to handle unbounded target densities.
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