论文标题
在亚指数类型损失下的吉布斯后浓度率
Gibbs posterior concentration rates under sub-exponential type losses
论文作者
论文摘要
贝叶斯后分布被广泛用于推断，但是它们对统计模型的依赖会带来一些挑战。特别是，可能有许多需要先前分布和后验计算的滋扰参数，以及可能严重的模型错误指定偏差的风险。另一方面，吉布斯后分布通过损失函数提供直接，原则性的，概率的推断，而不是基于模型的可能性。在这里，我们提供了简单的条件，以建立Gibbs后浓度率时，当损失函数为亚指数类型时。我们将这些一般结果应用于一系列实际相关的示例，包括平均回归，分位数回归和稀疏的高维分类。我们还将这些技术应用于医疗统计数据中的一个重要问题，即对个性化最小临床重要差异的估计。
Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior computations, plus a potentially serious risk of model misspecification bias. Gibbs posterior distributions, on the other hand, offer direct, principled, probabilistic inference on quantities of interest through a loss function, not a model-based likelihood. Here we provide simple sufficient conditions for establishing Gibbs posterior concentration rates when the loss function is of a sub-exponential type. We apply these general results in a range of practically relevant examples, including mean regression, quantile regression, and sparse high-dimensional classification. We also apply these techniques in an important problem in medical statistics, namely, estimation of a personalized minimum clinically important difference.
