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.

翻译：贝叶斯后天分布被广泛用于推断,但对统计模型的依赖造成了一些挑战。特别是,可能有许多骚扰性参数需要事先分布和后天计算,加上模型偏差的潜在严重风险。 Gibbs 后天分布则通过损失函数而不是模型可能性,直接、有原则、概率性地推断利息数量。在这里,当损失功能为亚爆炸性类型时,我们为确定Gibbs后天集中率提供了简单的充分条件。我们将这些一般性结果应用在一系列实际相关的例子中,包括平均回归、微积分回归和稀有的高维度分类。我们还将这些技术应用于医学统计中的一个重要问题,即估计个性化最低临床重要差异。