  Evidence-based knowledge of infectious disease burden, including prevalence,
incidence, severity and transmission, in different population strata and
locations, and possibly in real time, is crucial to the planning and evaluation
of public health policies. Direct observation of a disease process is rarely
possible. However, latent characteristics of an epidemic and its evolution can
often be inferred from the synthesis of indirect information from various
routine data sources, as well as expert opinion. The simultaneous synthesis of
multiple data sources, often conveniently carried out in a Bayesian framework,
poses a number of statistical and computational challenges: the heterogeneity
in type, relevance and granularity of the data, together with selection and
informative observation biases, lead to complex probabilistic models that are
difficult to build and fit, and challenging to criticize. Using motivating case
studies of influenza, this chapter illustrates the cycle of model development
and criticism in the context of Bayesian evidence synthesis, highlighting the
challenges of complex model building, computationally efficient inference, and
conflicting evidence.
