A NOTE ON PREDICTION SUFFICIENCY (ADEQUACY) AND SUFFICIENCY

Summary Let(X, A) be a measurable space and P a family of probability measures on A. Let B and C be sub s-algebras of A and B0 a sub s-algebra of B. It is shown that if B0 is prediction sufficient (adequate) for B with respect to C and P, and Y is sufficient for B0vC with respect to P then Y is sufficient for BvC with respect to P; that if P is homogeneous and (B0; B, C) is Markov for P, and B0vC is sufficient for Bvc with respect to P, then B0 is sufficient for B with respect to P; and by example that the Markov property is necessary for the latter proposition to hold.