论文标题
杰弗里斯 - 林德利悖论的目标贝叶斯方法
Objective Bayesian approach to the Jeffreys-Lindley paradox
论文作者
论文摘要
我们从客观的贝叶斯角度来考虑Jeffreys-Lindley悖论，试图找到代表问题中样本量完全无动于衷的先验。这意味着我们确保未知均值的先验和对$ t $统计量的先验预测与样本量无关。如果成功，这将导致与样本量无关并改善悖论的贝叶斯模型比较。不幸的是，这导致未知平均值的规模不变。但是，我们表明，截断的规模不变先验延迟了对样本量的依赖，这实际上可能很重要。最后，我们通过将量表不变的先验不当的事实联系起来，从而阐明了悖论。
We consider the Jeffreys-Lindley paradox from an objective Bayesian perspective by attempting to find priors representing complete indifference to sample size in the problem. This means that we ensure that the prior for the unknown mean and the prior predictive for the $t$-statistic are independent of the sample size. If successful, this would lead to Bayesian model comparison that was independent of sample size and ameliorate the paradox. Unfortunately, it leads to an improper scale-invariant prior for the unknown mean. We show, however, that a truncated scale-invariant prior delays the dependence on sample size, which could be practically significant. Lastly, we shed light on the paradox by relating it to the fact that the scale-invariant prior is improper.
