Ensored marginal a posteriori bayesian inference for signal models
Anthony Quinn · 2005
Using a strongly Bayesian formalism, it is shown that integration over the space spanned by the basis functions of a systematic hypothesis admits an objective complexity measure of the hypothesis. This results in the objective embodiment of Ockham's Razor within the marginal inference, via the Ockham Parameter Inference (OPI). The insight leads to a new Censored Marginal a Posteriori (CMaAP) estimation procedure which returns accurate estimates well be low the thresholds inherent in conventional Maximum Likelihood (ML) estimation. The procedure tests the status of an alternative-free hypothesis, unifying the detection and estimation tasks. The framework is readily extended to a multi-hypothesis environment where the OPI penalizes overly complex models. The selection and estimation tasks are unified into a consistent procedure which may be implemented without the need for numerical approximations. This confers a major computational saving over current approaches.