#### Chapter 5 Bayes Methods and Elementary Decision Theory

Theorem Every d ∈ D may be expressed as a convex combination of the the nonrandomized rules. Proof. Any d ∈ D may be represented as a k ×m matrix of ≥ 0realnumberswhosecolumns add to 1. The nonrandomized rules are those whose entries are 0's and 1's. Set d(ai,xj)=dij, d =(dij), 1 ≤ i ≤ k,1≤ j ≤ m.