arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 1101.4822astro-ph.IMastro-ph.CO
收藏

贝叶斯证据在天文学中的力量

The power of Bayesian evidence in astronomy

C. R. Jenkins, J. A. Peacock

摘要:

我们讨论了贝叶斯证据比或贝叶斯因子在天文学模型选择中的应用。我们把证据比作为一个统计量,并调查其分布在合奏的实验,考虑简单的分析例子和一些更现实的情况下,这需要数值模拟。我们发现,证据比是一个噪声统计,因此,它可能是不明智的,以决定接受或拒绝一个模型的证据比是否达到某个阈值的基础上。证据比所建议的比值与基于证据比的检验的功效或I类错误率没有明显的关系。这种检验的一般性能受到数据中的信噪比、假定的先验和被视为“决定性”的证据比中的阈值的强烈影响。考虑中的整套模式的全面性也非常重要。证据比方法在给定问题中的有用性可以在实验之前使用简单的模型和数值近似进行评估。在许多情况下,这种方法可以像复杂问题的成本更高的全面贝叶斯分析一样提供信息。

英文摘要:

We discuss the use of the Bayesian evidence ratio, or Bayes factor, for model selection in astronomy. We treat the evidence ratio as a statistic and investigate its distribution over an ensemble of experiments, considering both simple analytical examples and some more realistic cases, which require numerical simulation. We find that the evidence ratio is a noisy statistic, and thus it may not be sensible to decide to accept or reject a model based solely on whether the evidence ratio reaches some threshold value. The odds suggested by the evidence ratio bear no obvious relationship to the power or Type I error rate of a test based on the evidence ratio. The general performance of such tests is strongly affected by the signal to noise ratio in the data, the assumed priors, and the threshold in the evidence ratio that is taken as `decisive'. The comprehensiveness of the model suite under consideration is also very important. The usefulness of the evidence ratio approach in a given problem can be assessed in advance of the experiment, using simple models and numerical approximations. In many cases, this approach can be as informative as a much more costly full-scale Bayesian analysis of a complex problem.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑