Bayesian prediction with approximate frequentist validity
Bayesian prediction with approximate frequentist validity
复制标题
具有近似频率有效性的贝叶斯预测
DOI：
--
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
T. Sweeting
中科院分区：
文献类型：
--
作者：
G. Datta;R. Mukerjee;M. Ghosh;T. Sweeting
我们刻画先验渐近匹配的贝叶斯预测区域的后验覆盖概率与相应的频率覆盖概率。这是考虑后验分位数和参考未来观察的最高预测密度区域来完成的。所得到的先验被证明是不变的重新参数化。Jeffreys的事先在这方面的作用也进行了调查。它进一步表明，对于任何给定的先验，它可以选择一个区间的贝叶斯预测和频率覆盖概率渐近匹配。
We characterize priors which asymptotically match the posterior coverage probability of a Bayesian prediction region with the corresponding frequentist coverage probability. This is done considering both posterior quantiles and highest predictive density regions with reference to a future observation. The resulting priors are shown to be invariant under reparameterization. The role of Jeffreys' prior in this regard is also investigated. It is further shown that, for any given prior, it may be possible to choose an interval whose Bayesian predictive and frequentist coverage probabilities are asymptotically matched.