论文标题
通过高斯工艺略有限制的非参数贝叶斯推断
Marginally Constrained Nonparametric Bayesian Inference through Gaussian Processes
论文作者
论文摘要
非参数贝叶斯模型通常用作复杂数据的灵活且强大的模型。很多时候，统计学家可能对感兴趣的数据分布（例如其平均值或子集组件，与非参数cortrametric Prior的一部分，甚至不兼容）有更多的信息信念。然后，一个重要的挑战是将这种部分先验的信念纳入非参数贝叶斯模型中。在本文中，我们受到从业人员的设置的激励，在这些设置中，有有关正在建模的观测值的坐标子集的其他分布信息。我们的方法将此问题与条件密度建模联系起来。我们的主要思想是一个新颖的约束贝叶斯模型，基于对扰动函数的参数分布的扰动。我们还基于数据增强开发了相应的后验抽样方法。我们说明了我们提出的约束非参数贝叶斯模型在各种现实情况下的功效，包括建模环境和地震数据。
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components, that is not part of, or even compatible with, the nonparametric prior. An important challenge is then to incorporate this partial prior belief into nonparametric Bayesian models. In this paper, we are motivated by settings where practitioners have additional distributional information about a subset of the coordinates of the observations being modeled. Our approach links this problem to that of conditional density modeling. Our main idea is a novel constrained Bayesian model, based on a perturbation of a parametric distribution with a transformed Gaussian process prior on the perturbation function. We also develop a corresponding posterior sampling method based on data augmentation. We illustrate the efficacy of our proposed constrained nonparametric Bayesian model in a variety of real-world scenarios including modeling environmental and earthquake data.
