Many imaging systems are used to estimate a vector of parameters associated with the object being imaged. In many cases there are other parameters in the model for the imaging data that are not of interest for the task at hand. We refer to these as nuisance parameters and use them to form the components of the nuisance parameter vector. If we have a prior probability distribution function (PDF) for the nuisance parameter vector, then we may mariginalize over the nuisance parameters to produce a conditional PDF for the data that only depends on the parameters of interest. We will examine this approach to develop inequalities and approximations for the FIM when the data is affected by nuisance parameters.