Inference of fields defined in space and time from observational data is a core discipline in many scientific areas. This work approaches the problem in a Bayesian framework. The proposed method is based on statistically homogeneous random fields defined in space and time and demonstrates how to reconstruct the field together with its prior correlation structure from data. The prior model of the correlation structure is described in a non-parametric fashion and solely builds on fundamental physical assumptions such as space-time homogeneity, locality, and causality. These assumptions are sufficient to successfully infer the field and its prior correlation structure from noisy and incomplete data of a single realization of the process as demonstrated via multiple numerical examples.
翻译:从观测数据中确定空间和时间的字段的推断是许多科学领域的核心学科。这项工作在贝耶斯框架内处理问题。拟议方法基于在空间和时间上界定的统计均匀随机字段,并表明如何用数据来重建字段及其先前的相关性结构。先前的关联结构模型以非参数方式描述,仅以空间-时间同质性、地点和因果关系等基本物理假设为基础。这些假设足以成功地从多个数字实例所显示的单一实现过程的噪音和不完整数据中推断出字段及其先前的相关结构。