  This study performs parameter inference in a partial differential equations
system of pulmonary circulation. We use a fluid dynamics network model that
takes selected parameter values and mimics the behaviour of the pulmonary
haemodynamics under normal physiological and pathological conditions. This is
of medical interest as it enables tracking the progression of pulmonary
hypertension. We show how we make the fluids model tractable by reducing the
parameter dimension from a 55D to a 5D problem. The Delayed Rejection Adaptive
Metropolis (DRAM) algorithm, coupled with constraint nonlinear optimization is
successfully used to learn the parameter values and quantify the uncertainty in
the parameter estimates. To accommodate for different magnitudes of the
parameter values, we introduce an improved parameter scaling technique in the
DRAM algorithm. Formal convergence diagnostics are employed to check for
convergence of the Markov chains. Additionally, we perform model selection
using different information criteria, including Watanabe Akaike Information
Criteria.
