From an information-theoretic viewpoint, randomized statistical decision procedures are channels (or Markov kernels) that map observations to probability distributions over actions. Any sufficiently complex statistical decision procedure is a composition of simpler procedures, and it is of both theoretical and practical interest to obtain a precise characterization of the overall procedure from local descriptions of the constituent subprocedures. In this talk, I will show how this problem can be addressed using information-theoretic methods.