论文标题
通过几乎添加的热力学形式主义，贝叶斯后收敛损失功能
Bayes posterior convergence for loss functions via almost additive Thermodynamic Formalism
论文作者
论文摘要
统计推断可以看作是涉及输入信息和输出信息的信息处理，可更新有关某些未知参数的信念。我们考虑了贝叶斯框架，以从千古观测中推断动态系统，其中贝叶斯程序基于Gibbs后部推断，这是标准贝叶斯推断的决策过程概括，其中可能的可能性被损失功能的指数替换。在直接观察和几乎添加的损失函数的情况下，我们证明A后验的指数收敛性测量了一个极限度量。我们对直接观察的贝叶斯后融合的估计是相关的，并在K. McGoff，S。Mukherjee和A. Nobel的最新论文中扩展了这些估计。我们的方法利用了非添加热力学形式主义和较大的偏差特性而不是结合。
Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical systems from ergodic observations, where the Bayesian procedure is based on the Gibbs posterior inference, a decision process generalization of standard Bayesian inference where the likelihood is replaced by the exponential of a loss function. In the case of direct observation and almost-additive loss functions, we prove an exponential convergence of the a posteriori measures a limit measure. Our estimates on the Bayes posterior convergence for direct observation are related and extend those in a recent paper by K. McGoff, S. Mukherjee and A. Nobel. Our approach makes use of non-additive thermodynamic formalism and large deviation properties instead of joinings.
