It is shown that the first-order term of the asymptotic bias of the posterior mean is removed by a suitable choice of a prior density. In regular statistical models including exponential families, and linear and logistic regression models, such a prior is given by the squared Jeffreys prior. We also explain the relationship between the proposed prior distribution, the moment matching prior, and the prior distribution that reduces the bias term of the posterior mode.

翻译：本文证明，通过适当选择先验密度函数，可以消除后验均值渐近偏差的一阶项。在包含指数族、线性回归模型和逻辑回归模型在内的正则统计模型中，此类先验可由平方杰弗里斯先验给出。我们同时阐释了所提出的先验分布、矩匹配先验以及能够减少后验众数偏差项的先验分布之间的理论关联。