Priors for Reducing Asymptotic Bias of the Posterior Mean
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.
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