Increasing Returns to Data for a Bayesian Platform

The paper solves the optimal sampling problem of a decision-maker that wants to predict a target variable. We prove the existence of complementarities between the sample size and the number of explanatory variables in a data set. We show that the optimal dimensions of the data set reflect the bias/variance trade-off. We prove there are always entry barriers in the form of a minimum number of users under which it is not optimal to collect any data. Above this threshold, the model endogenously generates S-shaped returns to the number of platform users: when users are not too many, there always are locally increasing returns to scale