Is the Jeffreys' scale a reliable tool for Bayesian model comparison in cosmology?
Is the Jeffreys' scale a reliable tool for Bayesian model comparison in cosmology?
复制标题
DOI：
10.1088/1475-7516/2013/08/036
复制
发表时间：
2012-10
影响因子：
6.4
通讯作者：
S. Nesseris;J. García-Bellido
中科院分区：
文献类型：
--
作者：
S. Nesseris;J. García-Bellido
我们正在进入一个宇宙学的进步是由数据驱动的时代，替代模型将不得不根据一些一致的标准进行比较和排除。最保守和最广泛使用的方法是贝叶斯模型比较。在本文中，我们显式地计算所有模型的贝叶斯因子，这些模型相对于它们的参数是线性的。我们这样做是为了测试所谓的杰弗里斯尺度，并分析确定它的预测在一个简单的情况下有多准确，我们完全理解并可以分析计算一切。我们还讨论了嵌套模型的情况下，例如一个与M1和另一个与M2和M1参数，我们推导出解析表达式的贝叶斯因子和图的优点，定义为模型参数的置信度轮廓的倒数区域。所有这些机制和使用一个明确的例子，我们证明了Jeffreys的规模的阈值性质是不是一个“一刀切”的可靠工具模型比较，它可能会导致有偏见的结论。此外，我们讨论了选择正确的基础上的背景下，模型是线性的，其参数和基础如何影响参数估计和派生的约束条件的重要性。
We are entering an era where progress in cosmology is driven by data, and alternative models will have to be compared and ruled out according to some consistent criterium. The most conservative and widely used approach is Bayesian model comparison. In this paper we explicitly calculate the Bayes factors for all models that are linear with respect to their parameters. We do this in order to test the so called Jeffreys' scale and determine analytically how accurate its predictions are in a simple case where we fully understand and can calculate everything analytically. We also discuss the case of nested models, e.g. one with M1 and another with M2⊃M1 parameters and we derive analytic expressions for both the Bayes factor and the figure of Merit, defined as the inverse area of the model parameter's confidence contours. With all this machinery and the use of an explicit example we demonstrate that the threshold nature of Jeffreys' scale is not a ``one size fits all'' reliable tool for model comparison and that it may lead to biased conclusions. Furthermore, we discuss the importance of choosing the right basis in the context of models that are linear with respect to their parameters and how that basis affects the parameter estimation and the derived constraints.