  A lower bound is an important tool for predicting the performance that an
estimator can achieve under a particular statistical model. Bayesian bounds are
a kind of such bounds which not only utilizes the observation statistics but
also includes the prior model information. In reality, however, the true model
generating the data is either unknown or simplified when deriving estimators,
which motivates the works to derive estimation bounds under modeling mismatch
situations. This paper provides a derivation of a Bayesian Cram\'{e}r-Rao bound
under model misspecification, defining important concepts such as pseudotrue
parameter that were not clearly identified in previous works. The general
result is particularized in linear and Gaussian problems, where closed-forms
are available and results are used to validate the results.
