Discussion of 'A novel approach to the analysis of spatial and functional data over complex domains'

Abstract

The dependency structure of complex data is always a challenge in formulating and yielding accurate estimates. Dr Laura M. Sangalli’s paper offers a well-developed method to formulate the boundary spatial dependency by using the PDE regularization term, but other forms of spatial or spatiotemporal dependencies also need more efforts to solve. After a more accurate model and estimation, monitoring can be further conducted to contribute more practical value to the process control. The two most popular ways to capture the spatiotemporal dependencies can be summarized as follows: the first is to introduce regularization terms according to the auxiliary information; the second is to form data in tensor form, especially high-dimensional data, and then apply the corresponding tensor analysis method. Last but not least, after performing accurate estimation, a monitoring statistic can be constructed and the monitoring scheme applied to calculate the control limit and start the quality control process.