论文标题
广义贝叶斯推断中学习率选择方法的比较
A comparison of learning rate selection methods in generalized Bayesian inference
论文作者
论文摘要
通用的贝叶斯后分布是通过在与先前的贝叶斯公式结合之前在可能性上施加分数力来形成的。这种分数能力通常被视为潜在模型错误指定偏差的补救措施，称为学习率，并且在最近的文献中已经提出了许多数据驱动的学习率选择方法。这些建议中的每一个都有不同的重点，他们旨在实现的目标不同，这使得它们难以比较。在本文中，我们在各种错误指定的模型方案中对这些学习率选择方法进行直接对头比较，而对于几种相关指标，尤其是通用贝叶斯可信区域的覆盖概率。在某些示例中，所有方法的表现都很好，而在另一些示例中，错误指定太严重而无法克服，但是我们发现所谓的广义后校准算法倾向于在可靠的区域覆盖范围方面表现优于其他算法。
Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, which is often viewed as a remedy for potential model misspecification bias, is called the learning rate, and a number of data-driven learning rate selection methods have been proposed in the recent literature. Each of these proposals has a different focus, a different target they aim to achieve, which makes them difficult to compare. In this paper, we provide a direct head-to-head comparison of these learning rate selection methods in various misspecified model scenarios, in terms of several relevant metrics, in particular, coverage probability of the generalized Bayes credible regions. In some examples all the methods perform well, while in others the misspecification is too severe to be overcome, but we find that the so-called generalized posterior calibration algorithm tends to outperform the others in terms of credible region coverage probability.
