example biomarker assays in biomedical studies, enable the generation of rich datasets. It is increasingly common for researchers to have access to multiple ($K > 1$) studies, or more generally sets of data, able to answer the same or similar scientific questions [@klein2014data; @kannan2016public; @manzoni2018genome]. Although datasets from multiple studies may contain the same outcome variable $Y$ and covariates $X$ (for example, patient survival and pre-treatment prognostic profiles in clinical studies), the $(X, Y)$ joint distributions $P_1, \ldots, P_K$ are typically different, due to distinct study populations, study designs and technological artifacts [@simon2003pitfalls; @rhodes2004large; @patil2015test; @sinha2017assessment]. In this article, we focus on the task of developing prediction models using multiple datasets, accounting for the heterogeneity across the $(P_k, k = 1,\ldots,K)$ study-specific distributions. We introduce a distinction between two classes of *prediction functions* (PFs) depending on the goal of the prediction problem in the multi-study setting: *generalist* and *specialist* prediction functions.

Generalist predictions are directed to hypothetical future studies $K+1, K+2, \ldots$. The training strategy to develop a generalist prediction function depends on relations and similarities between studies. For example, the study-specific geographic areas or assays can be relevant in the development of prediction models. If studies are considered exchangeable, 