Comparison of experiments when the parameter space is finite

The convex function criterion for "being more informative" for k-decision problems is-in Section 2-generalized to a convex function criterion for edeficiency for k-decision problems. The particular case of comparison by testing problems is discussed in Section 3. A theorem of Blackwell on comparison of dichotomies is generalized and a problem on products of experiments raised by Blackwell is settled by counter-example. Pairwise comparison of experiments and minimal combinations of experiments are discussed. The problem of composing and decomposing experiments by mixtures is treated in Section 4. It is shown that any experiment with finite parameter space is a mixture of complete experiments, and the complete experiments are characterized.