  We address the problem of parameter estimation in models of systems biology
from noisy observations. The models we consider are characterized by
simultaneous deterministic nonlinear differential equations whose parameters
are either taken from in vitro experiments, or are hand-tuned during the model
development process to reproduces observations from the system. We consider the
family of algorithms coming under the Bayesian formulation of Approximate
Bayesian Computation (ABC), and show that sensitivity analysis could be
deployed to quantify the relative roles of different parameters in the system.
Parameters to which a system is relatively less sensitive (known as sloppy
parameters) need not be estimated to high precision, while the values of
parameters that are more critical (stiff parameters) need to be determined with
care. A tradeoff between computational complexity and the accuracy with which
the posterior distribution may be probed is an important characteristic of this
class of algorithms.
