COMPARING BAYESIAN MODELS IN THE ABSENCE OF GROUND TRUTH

Modern signal processing methods rely strongly on Bayesian statistical models to solve challenging problems. This paper considers the objective comparison of two alternative Bayesian models, for scenarios with no ground truth available, and with a focus on model selection. Existing model selection approaches are generally difficult to apply to signal processing because they are unsuitable for models with priors that are improper or vaguely informative, and because of challenges related to high dimensionality. This paper presents a general methodology to perform model selection for models that are high-dimensional and that involve proper, improper, or vague priors. The approach is based on an additive mixture meta-model representation that encompasses both models and which concentrates on the model that fits the data best, and relies on proximal Markov chain Monte Carlo algorithms to perform high-dimensional computations efficiently. The methodology is demonstrated on a series of experiments related to image resolution enhancement with a total-variation prior.