This proposal attempts to follow in Allan Birnbaum's tradition by using Bayesian ideas to show that his mental test model possesses even broader applicability than previously realized. Birnbaum's two significant contributions to the theories of statistics and educational testing are: (1) the proof that the sufficiency and conditionality principles together imply the liklihood principle, thus justifying conditional or Bayesian inference when compared with frequentist inference; and (2) the mental test model introduced by Lord and Novick. A conditional maximization procedure is used here to approximate numerical integrations, thus broadening the scope of Bayesian inference and model checking. (Author/GDC)