论文标题
嵌套的采样和可能性高原
Nested Sampling And Likelihood Plateaus
论文作者
论文摘要
嵌套采样的主要思想是通过在单位线$ [0,1] $上不可或缺的参数空间$ [0,1] $替换高维的可能性积分，而在合适的转换方面采用了推动力。对于此替代，通常隐含或明确地假设先前的样品在通过此转换绘制绘制后沿该单位线均匀分布。我们表明，这个假设是错误的，尤其是在具有高原的可能性功能的情况下。然而，我们表明，嵌套采样制定的替代作用是因为我们提出的更有趣的原因。尽管这意味着在分析上，嵌套的采样可以在可能性函数中处理高原，但该算法的实际性能在这种设置下遭受了损失，该方法无法适当地近似证据，均值和差异。我们建议通过一个简单的分解想法来实现嵌套采样的强大实现，该想法明显地克服了这个问题。
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $Ω$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation. For this substitution, it is often implicitly or explicitly assumed that samples from the prior are uniformly distributed along this unit line after having been mapped by this transformation. We show that this assumption is wrong, especially in the case of a likelihood function with plateaus. Nevertheless, we show that the substitution enacted by nested sampling works because of more interesting reasons which we lay out. Although this means that analytically, nested sampling can deal with plateaus in the likelihood function, the actual performance of the algorithm suffers under such a setting and the method fails to approximate the evidence, mean and variance appropriately. We suggest a robust implementation of nested sampling by a simple decomposition idea which demonstrably overcomes this issue.
