A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion
A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion
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DOI：
10.1080/01621459.1995.10476592
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发表时间：
1995-09
影响因子：
3.7
通讯作者：
R. Kass;L. Wasserman
中科院分区：
文献类型：
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作者：
R. Kass;L. Wasserman
为了计算在干扰参数β存在的情况下检验H 0: ψ = ψ0的贝叶斯因子，必须选择原假设和备假设下的先验。在贝叶斯估计中，一个重要的问题是定义自动的或“参考”方法，仅基于模型的结构来确定先验。在这篇文章中，我们应用启发式的方法，取ψ的先验信息量等于单次观测中的信息量。然后，在将β转换为与ψ“零正交”之后，我们在零假设和备选假设下使β的边际先验相等。这样做，并取ψ的先验为正态，我们发现贝叶斯因子的对数可以用Schwarz准则近似，误差为O阶p (n−1 / 2)，而不是通常的O阶p(1)。这一结果表明，施瓦茨准则应该为贝叶斯检验问题提供合理的近似解，至少当假设嵌套时是这样。当……
Abstract To compute a Bayes factor for testing H 0: ψ = ψ0 in the presence of a nuisance parameter β, priors under the null and alternative hypotheses must be chosen. As in Bayesian estimation, an important problem has been to define automatic, or “reference,” methods for determining priors based only on the structure of the model. In this article we apply the heuristic device of taking the amount of information in the prior on ψ equal to the amount of information in a single observation. Then, after transforming β to be “null orthogonal” to ψ, we take the marginal priors on β to be equal under the null and alternative hypotheses. Doing so, and taking the prior on ψ to be Normal, we find that the log of the Bayes factor may be approximated by the Schwarz criterion with an error of order O p (n −½), rather than the usual error of order O p (1). This result suggests the Schwarz criterion should provide sensible approximate solutions to Bayesian testing problems, at least when the hypotheses are nested. When...