论文标题
近似贝叶斯方法与先前鲁棒性之间的二元性
Duality between Approximate Bayesian Methods and Prior Robustness
论文作者
论文摘要
在本文中，我们表明近似贝叶斯方法与先前的鲁棒性之间存在联系。我们表明，通常被认为是与可能性的近似值，这是由于模拟数据（如近似贝叶斯计算方法（ABC）方法中的模拟数据），或者是由于可能与可能性的功能近似所致，也可以将其视为先前鲁棒性的隐式练习。我们首先为有足够的统计数据，确定其数学属性并显示的简单示例的情况下定义了两个新类别的先验，并显示这些类别的先验也可以用于获得通过实现ABC获得的后验分布。然后，我们概括并定义了在非常笼统的情况下适用的另外两个先验类别。一个没有足够的统计信息，另一个使用功能近似近似可能的可能性。然后，我们讨论此处提出的类的解释和启发方面以及它们的潜在应用和可能的计算益处。这些类别确定了近似贝叶斯推论与广泛类别的贝叶斯推理方法的鲁棒性之间的二元性。
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate Bayesian Computation (ABC) methods or due to the functional approximation to the likelihood, can instead also be viewed upon as an implicit exercise in prior robustness. We first define two new classes of priors for the cases where the sufficient statistics is available, establish their mathematical properties and show, for a simple illustrative example, that these classes of priors can also be used to obtain the posterior distribution that would be obtained by implementing ABC. We then generalize and define two further classes of priors that are applicable in very general scenarios; one where the sufficient statistics is not available and another where the likelihood is approximated using a functional approximation. We then discuss the interpretation and elicitation aspects of the classes proposed here as well as their potential applications and possible computational benefits. These classes establish the duality between approximate Bayesian inference and prior robustness for a wide category of Bayesian inference methods.
