The performance of Bayesian estimators in the superresolution of signal parameters

The complete Bayesian inference for the general nonlinear signal model is derived, and the available policies of joint and marginal estimation for the nonlinear parameters are compared. The joint (and maximum likelihood) estimator fits the model to the data using a minimum error norm criterion, returning spurious estimates in superresolution and high noise regimes. In contrast, the marginal estimator trades data evidence against the desideratum of a simpler model. In the absence of data support for the model, an inference of model redundancy is made via a data-independent term in the marginal estimator, providing robust behavior in stressful regimes. This term has previously been ignored in the literature on estimation but offers compelling grounds for the adoption of the marginal Bayesian inference strategy