The foremost challenge for statistical science in the twenty-first century is to sustain and grow the place of statistical method (singular) as an integral component of scientific method. I shall offer a personal response to this challenge in the specific setting of spatio-temporal point process data.
Generic methods of analysis for spatio-temporal point process data are now well developed and accessible as R packages. Using examples from the biomedical and health sciences, I will argue that as the twenty-first century progresses, effective strategies for modelling and inference will increasingly depend on close collaboration between statisticians and subject-matter experts.
Risking over-simplification, I will make a distinction between: empirical models, which predominate within the data science community and are well-suited to problems where the goal is prediction, the data are abundant and the underlying scientific process is poorly understood; and mechanistic models, which are indicated when the goal is estimation, the data are sparse and the underlying scientific process is well understood.