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Improving the efficiency and robustness of nested sampling using posterior repartitioning

机译：使用后验重新分配提高嵌套采样的效率和鲁棒性

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摘要

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings of the assumed prior distribution, this can lead to extremely inefficient exploration of the resulting posterior by nested sampling (NS) algorithms, with unnecessarily high associated computational costs. Simple solutions such as broadening the prior range in such cases might not be appropriate or possible in real-world applications, for example when one wishes to assume a single standardised prior across the analysis of a large number of datasets for which the true values of the parameters of interest may vary. This work therefore introduces a posterior repartitioning (PR) method for NS algorithms, which addresses the problem by redefining the likelihood and prior while keeping their product fixed, so that the posterior inferences and evidence estimates remain unchanged but the efficiency of the NS process is significantly increased. Numerical results show that the PR method provides a simple yet powerful refinement for NS algorithms to address the issue of unrepresentative priors.
机译：在实际的贝叶斯推理应用程序中，有关感兴趣参数的先前假设可能无法代表给定数据集的实际值。特别是，如果可能性集中在假设的先验分布的边缘，则可能导致嵌套抽样（NS）算法对所得后验的效率极低，并且不必要地增加了相关的计算成本。在实际应用中，例如在这种情况下扩大先验范围之类的简单解决方案可能不适用或不可能，例如，当您希望在分析大量数据集的真实值时假设一个标准化先验时，感兴趣的参数可能会有所不同。因此，这项工作为NS算法引入了后验重分配（PR）方法，该方法通过重新定义可能性和先验值，同时保持其乘积固定，从而解决了该问题，因此后验推论和证据估计保持不变，但NS过程的效率非常高增加。数值结果表明，PR方法为NS算法提供了一个简单而强大的改进，以解决先验性代表问题。

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