Some insights on checking conditional independence in functional graphical models

In recent years, there has been growing interest in the study of conditional independencies in functional data across various areas, including biomedical research, economics, and environmental sciences. The objective of this work is to provide insights into two of the main frameworks in the frequentist literature on functional Gaussian graphical models, focusing on their methodological contributions and practical implementation. Specifically, we provide a critical analysis of the graph selection strategies and the management of tuning parameters involved in the conditional independence structural learning process. A simulation study accompanies the analysis.