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The Research Training Group 1644 "Scaling Problems in Statistics" was funded by the Geman Research Foundation (DFG) from October 2010 to September 2019.

The Research Training Group (RTG) focused on "Scaling Problems in Statistics'' as a general framework for developing, extending and applying statistical methodology related to scaling problems. In a broad sense, the notion of scale and associated scaling problems can be understood as an encompassing concept for challenges in empirical analysis where the units of observation behave differently when studying them on different scales. This implies that the measurement scale, and in particular the central properties of resolution and extent, have to be taken into account in statistical analyses. Thereby scales can represent very different concepts, ranging from spatial and temporal scales as the most obvious examples, over different levels of aggregation (e.g. from individuals over households to communities or states), to different levels of genetic information (e.g. in a functional scale from single base pairs over genes to pathways of genes).

In this RTG, we have been treating scaling as a particular type of contextual information that has to be taken into account appropriately to provide meaningful results for research questions, such as "How does the association of animal and plant abundance depend on ecological conditions?'', "What impact has the price of one product on that of another?'' or "How does genetic variation impact susceptibility towards a specific disease or the prediction of a genetically affected trait?'' In all these cases, the result crucially depends on the scale chosen for the statistical analysis. Statistical methodology formed the core of the RTG, providing the interface between the considered areas of application (ecology, economics, genetics). This setup allowed us to stimulate methodological innovations based on challenging applications, to transfer general methodological innovations to the applied areas, and to foster the transfer of methods between the different areas of application. The methodological framework for the RTG was formed by mixed models, spatial statistics and distributional regression, roughly corresponding to the notions of hierarchical scales (mixed models), spatial scales (spatial statistics), and the measurement scale (distributional regression), respectively. For some specific projects, additional methodological topics such as networks or kernel regression were considered in addition.

The interdisciplinarity of the research agenda of the RTG was also well reflected in the qualification program. The first core element, introductions to mixed models and spatial statistics, provided the PhD students with advanced knowledge in statistical methods dealing with scaling problems. Building on this common ground, further subjects were introduced in the form of specialization courses, research colloquia, and research seminars. A further important ingredient in qualification were courses on key competencies, including mandatory courses on "Diversity Competence'', "Good Scientific Practice'' and "Collecting and Archiving Research Data''.

Based on the experience from two successful funding phases and three cohorts of PhD students, we have convincing evidence for the stimulating environment that an interdisciplinary group with a methods-driven research and qualification agenda provides for young scientists. The PhD alumni of the RTG report very positively about the experiences they gained from their work in the RTG and in particular highlight the relevance of interdisciplinary collaboration and communication for their future careers in academia as well as in companies. We were able to develop important and innovative research results, where the interdisciplinary setup was stimulating the development of methods via exposure to challenging applied research problems on the one hand and the transfer of novel methods to applications on the other hand.