比较天体物理模型与观测的一致性检验
Consistency Tests for Comparing Astrophysical Models and Observations
AI总结：
本文提出一致性检验（ConTESTs）方法，结合非参数方法与距离度量，以模型无关方式评估天体物理模型与观测的一致性，并通过模拟和天文学案例验证其有效性。
摘要：
在天文学中，有机会通过统计技术来加强模型验证的实践，特别是考虑测量误差的不确定性。虽然模型通常用于描述观测，但在某些情况下两者之间缺乏一致性。当模型源自不完整的理论、没有更优拟合模型可用或测量不确定性未被正确考虑时，就可能出现这种情况。然而，通过应用以模型无关的方式评估观测与天体物理模型之间一致性的特定检验，可以解决这一问题。本文提出的一致性检验（ConTESTs）结合了非参数方法和距离度量，以获得一个检验统计量来评估天体物理模型与观测的接近程度。为了对一致性假设得出结论，采用了一种基于模拟的方法。具体而言，我们构建了两个用于密度模型的检验和两个用于回归模型的检验，可根据具体情况和所需的检验功效选用。我们使用ConTEST检验了合成示例，以确定这些检验的有效性，并为建模过程中使用它们提供指导。我们还将ConTEST应用于多个天文学案例，识别出哪些模型是一致的，如果不一致，则识别出被拒绝的可能原因。
英文摘要：
In astronomy, there is an opportunity to enhance the practice of validating models through statistical techniques, specifically to account for measurement error uncertainties. While models are commonly used to describe observations, there are instances where there is a lack of agreement between the two. This can occur when models are derived from incomplete theories, when a better-fitting model is not available or when measurement uncertainties are not correctly considered. However, with the application of specific tests that assess the consistency between observations and astrophysical models in a model-independent way, it is possible to address this issue. The consistency tests (ConTESTs) developed in this paper use a combination of non-parametric methods and distance measures to obtain a test statistic that evaluates the closeness of the astrophysical model to the observations. To draw conclusions on the consistency hypothesis, a simulation-based methodology is performed. In particular, we built two tests for density models and two for regression models to be used depending on the case at hand and the power of the test needed. We used ConTEST to examine synthetic examples in order to determine the effectiveness of the tests and provide guidance on using them while building a model. We also applied ConTEST to various astronomy cases, identifying which models were consistent and, if not, identifying the probable causes of rejection.
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