  This paper offers a qualitative insight into the convergence of Bayesian
parameter inference in a setup which mimics the modeling of the spread of a
disease with associated disease measurements. Specifically, we are interested
in the Bayesian model's convergence with increasing amounts of data under
measurement limitations. Depending on how weakly informative the disease
measurements are, we offer a kind of `best case' as well as a `worst case'
analysis where, in the former case, we assume that the prevalence is directly
accessible, while in the latter that only a binary signal corresponding to a
prevalence detection threshold is available. Both cases are studied under an
assumed so-called linear noise approximation as to the true dynamics. Numerical
experiments test the sharpness of our results when confronted with more
realistic situations for which analytical results are unavailable.
