论文标题
部分可观测时空混沌系统的无模型预测
A Study on the Power Parameter in Power Prior Bayesian Analysis
论文作者
论文摘要
事实证明，权力及其变化是贝叶斯推论中有用的一类信息，因为它们的灵活性通过将历史数据的可能性提高到分数能力δ来结合历史信息。基于原始功率先验的边际可能性及其变化（归一化功率先验）的推导，以先前的预测分布的形式引入了缩放因子C（δ），具有功率的可能性。在本文中，我们表明，对于常规使用的初始先验，某些正δ可能是无限的，这将改变可允许的功率参数集。在文献中，这个结果似乎几乎完全被忽略了。然后，我们说明，当模型参数的初始先验不正确时，这种现象可能会危及功率先验下的后推断。本文的主要发现表明，当建议的借款水平接近0时，应特别注意，而实际最佳限额可能低于建议的价值。我们将普通线性模型作为说明目的的示例。
The power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a fractional power δ. The derivation of the marginal likelihood based on the original power prior,and its variation, the normalized power prior, introduces a scaling factor C(δ) in the form of a prior predictive distribution with powered likelihood. In this paper, we show that the scaling factor might be infinite for some positive δ with conventionally used initial priors, which would change the admissible set of the power parameter. This result seems to have been almost completely ignored in the literature. We then illustrate that such a phenomenon may jeopardize the posterior inference under the power priors when the initial prior of the model parameters is improper. The main findings of this paper suggest that special attention should be paid when the suggested level of borrowing is close to 0, while the actual optimum might be below the suggested value. We use a normal linear model as an example for illustrative purposes.
