具有扩散先验的贝叶斯假设检验:我们能既吃蛋糕又吃蛋糕吗?

Pub Date : 2024-03-19 DOI:10.1111/anzs.12410
J. T. Ormerod, M. Stewart, W. Yu, S. E. Romanes
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引用次数: 0

摘要

我们提出了一类新的贝叶斯假设检验先验,并将其命名为 "蛋糕先验"。这些先验值规避了杰弗里斯-林德利悖论(又称巴特利悖论),这是一个与使用扩散先验值导致不合理统计推断有关的问题。蛋糕先验允许使用扩散先验(拥有自己的蛋糕),同时实现理论上合理的推论(吃蛋糕)。我们针对各种常见情况的贝叶斯假设检验演示了这种方法。由此得出的贝叶斯检验统计量采用了惩罚似然比检验统计量的形式。在典型的正则条件下,我们证明了基于饼先验的贝叶斯假设检验是切尔诺夫一致的,即渐进地达到零I型和II型误差概率。我们还讨论了林德利悖论,并论证了随着样本量的增加,该悖论出现的概率很小,甚至消失。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Bayesian hypothesis tests with diffuse priors: Can we have our cake and eat it too?

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Bayesian hypothesis tests with diffuse priors: Can we have our cake and eat it too?

We propose a new class of priors for Bayesian hypothesis testing, which we name ‘cake priors’. These priors circumvent the Jeffreys–Lindley paradox (also called Bartlett's paradox) a problem associated with the use of diffuse priors leading to nonsensical statistical inferences. Cake priors allow the use of diffuse priors (having one's cake) while achieving theoretically justified inferences (eating it too). We demonstrate this methodology for Bayesian hypotheses tests for various common scenarios. The resulting Bayesian test statistic takes the form of a penalised likelihood ratio test statistic. Under typical regularity conditions, we show that Bayesian hypothesis tests based on cake priors are Chernoff consistent, that is, achieve zero type I and II error probabilities asymptotically. We also discuss Lindley's paradox and argue that the paradox occurs with small and vanishing probability as sample size increases.

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