论文标题
顺势疗法的先验？
Homeopathic priors?
论文作者
论文摘要
复合假设检验的问题是在贝叶斯在混乱的背景下检测弱目标信号的背景下考虑的问题。 （一个具体的示例是在多光谱图像中检测子像素目标。）在此模型中，目标强度（称为$ a $）是一个未知参数，并且可以通过在可能的参数值上纳入先验来解决知识的缺乏。检测器的性能取决于先验的选择，并且 - 在低位目标丰度下实现更好的性能的动机 - 研究了一个先验家族，其中奇异的重量与$ a \ to $ a \ 0 $限制有关。仔细治疗这种限制过程会导致一种情况，在这种情况下，无限重量的先前组成部分具有非平凡的影响。对于顺势疗法药物也提出了类似的主张。
The problem of composite hypothesis testing is considered in the context of Bayesian detection of weak target signals in cluttered backgrounds. (A specific example is the detection of sub-pixel targets in multispectral imagery.) In this model, the target strength (call it $a$) is an unknown parameter, and that lack of knowledge can be addressed by incorporating a prior over possible parameter values. The performance of the detector depends on the choice of prior, and -- with the motivation of enabling better performance at low target abundances -- a family of priors are investigated in which singular weight is associated with the $a\to 0$ limit. Careful treatment of this limiting process leads to a situation in which components of the prior with infinitesimal weight have nontrivial effects. Similar claims have been made for homeopathic medicines.
