Checking for model failure and for prior-data conflict with the constrained multinomial model.

Multinomial models can be difficult to use when constraints are placed on the probabilities. An exact model checking procedure for such models is developed based on a uniform prior on the full multinomial model. For inference, a nonuniform prior can be used and a consistency theorem is proved concerning a check for prior-data conflict with the chosen prior. Applications are presented and a new elicitation methodology is developed for multinomial models with ordered probabilities.

Characterizing the structure of preserved information in quantum processes.

We introduce a general operational characterization of information-preserving structures-encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes-by demonstrating that they are isometric to fixed points of unital quantum processes. Using this, we show that every information-preserving structure is a matrix algebra. We further establish a structure theorem for the fixed states and observables of an arbitrary process, which unifies the Schrödinger and Heisenberg pictures, places restrictions on physically allowed kinds of information, and provides an efficient algorithm for finding all noiseless and unitarily noiseless subsystems of the process.