论文标题
Banach空间中非参数贝叶斯逆问题的地图估计器
MAP estimators for nonparametric Bayesian inverse problems in Banach spaces
论文作者
论文摘要
为了严格定义一般Banach空间有价值参数的非参数贝叶斯逆问题的最大A-Posteriori估计器，我们得出了某些先前假定但在小球概率上未经证实的界限。这使我们能够在非常温和的假设下证明在Banach空间设置中存在地图估计器。迄今为止，仅在希尔伯特空间环境中存在类似的陈述（就作者所知），这缩小了文献中的重要差距。
In order to rigorously define maximum-a-posteriori estimators for nonparametric Bayesian inverse problems for general Banach space valued parameters, we derive and prove certain previously postulated but unproven bounds on small ball probabilities. This allows us to prove existence of MAP estimators in the Banach space setting under very mild assumptions on the loglikelihood. As a similar statement so far (as far as the author is aware) only existed in the Hilbert space setting, this closes an important gap in the literature.
