The author adopts a strong Bayesian philosophy and derives the marginal inference for the nonlinear parameters in a general deterministic signal model, having integrated over the linear terms. The marginal inference is shown to embody Ockham's razor in an objective manner via the Ockham parameter inference. From this, a new definition of hypothesis complexity, is proposed. The marginal inference provides a means of testing the status of an alternative-free hypothesis, thereby unifying the detection and estimation tasks. Robust estimates may then be inferred below the thresholds for maximum likelihood estimation. The analysis is extended to a multi-hypothesis environment, using the example of a periodic model of unknown order. The fundamental frequency is estimated in a unified procedure which can either (i) simultaneously estimate the model order, or (ii) marginalize analytically over the model order. Both techniques confer improved inferential consistency and a much reduced numerical load when compared with the popular evidence-based technique, which is also described.
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