Suppose there are n families selected through ascertainment sampling. Letting the k th ascertained family have s k siblings, we assume that there are r k affected and ak ascertained. In Crow's **data** s k vary from 1 to 10. The simplest ascertainment model specifies that   k = 1, . . . , n. This is the basic ignorable selection model. The a k are really covariates, and this leads to improved precision. Thus, the joint probability mass function of (a k , r k ) is
( , | , ) (1 ) (1 ) , k k k k k k k k r s r a r a k k k k s r p a r p p p r a π π π − −     = − −        (1)
a k = 0,...,r k , r k = 0,...,s k , k= 1,...,n. Note that (1) provides the likelihood for any family without conditioning on whether it is ascertained or not.