Understanding the Sampling Bias: A Case Study on NBA Drafts

In several real data applications a biased sample arises naturally from the selection procedure. Recently, Economou et al. (Biom J 62: 238–249, 2020) used the concept of bivariate weighted distributions and proposed four different families of weight functions to describe cases in which the bias in a bivariate sample is caused by adopting sampling schemes that result in over- or under-representation of individuals with specific properties in the sample. The current paper focuses on revealing the contribution of each variable to the bias in the bivariate sample. More specifically, under the Bayesian perspective, Approximate Bayesian Computation methods are used to sample approximately from the posterior distribution, and the Deviance Information Criterion is employed to compare the fit of the models obtained by using different weight functions. The proposed method is illustrated to a real data set concerning NBA draft players.