Abstract: Selection models are appropriate when the probability that a potential datum enters the sample is a nondecreasing function of the numeric value of the datum. It is rarely justifiable to model this function, called the weight function, with a specific parametric form, but appealing to model it with a nonparametric prior centered around a parametric form. The Bayesian analysis with a Dirichlet process prior for the weight function is considered and it is proved that the posterior is consistent under the weak topology.
Key words and phrases: Dirichlet process, posterior consistency, selection model, weight function.