Problem
Suppose we have a given model P(X | θ) on a set of variable X = {X1, . . . , Xn}, and some incomplete data. Suppose we introduce additional variables Y = {Y1, . . . , Yn} so that Yi has the value 1 if Xi is observed and 0 otherwise. We can extend the data, in the obvious way, to include complete observations of the variables Y. Show how to augment the model to build a model P(X,Y| θ, θ') = P(X|θ)P(Y| X, θ') so that it satisfies the missing at random assumption.