Minimum Bias Priors for Estimating Parameters of Additive Terms in State-Space Models

We treat the problem of estimating parameters of additive terms, sometimes called bias terms, in state-space models. We consider models that depend linearly on the state but possibly nonlinearly on the parameters, where both the state and observation are corrupted by additive noise. A prior density for the parameters is introduced that, when combined with the likelihood function to form a posterior density, minimizes the bias of the posterior mean. The result is a useful prior based on ignorance. Two examples and simulations illustrate the use of the prior.