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CPS1916 Erica P. et al.
This is certainly a major advantage of using Bayesian hierarchical models,
which provide a general adaptable way to formulate a broad range of models
and structures, as in our case measurement error or dependency structures,
and more generally any additional random effect which might be needed in
the analysis. Moreover, the use of a Bayesian framework allows to incorporate
prior knowledge in the analysis, for example about the error component and
parameters, as well as to reflect the prior uncertainty in the posterior
distributions of parameters of interest. Of course, this requires some
knowledge about the error component, in order to properly formulate the
measurement error level and to assign reasonable priors. Note that this
requirement is not specific to the Bayesian framework, but rather to any error
modelling strategies. In fact, it is always necessary to know the error structure
(i.e. classical measurement error and its distribution), as well as the error
variance, in order to formulate an identifiable error model (Gustafson, 2005).
In practice, it is not always straightforward to obtain such information, and
often assumptions about the error distribution and parameters are vague or
potentially incorrect. The advantage of Bayesian models is that the uncertainty
in such assumptions can easily be accounted for and propagated to posterior
distributions of corrected estimates.

References
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2. Dominici, F., S. Zeger, and J. Samet (2000). “A measurement error model
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3. Edwards, J.K., and A.P. Keil. 2017. “Measurement Error and Environmental
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4. Goldman, G.T., J.A. Mulholland, A. G. Russell, M.J. Strickland, M. Klein, L.A.
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