  The inherent behavioral variability exhibited by stochastic biochemical
systems makes it a challenging task for human experts to manually analyze them.
Computational modeling of such systems helps in investigating and predicting
the behaviors of the underlying biochemical processes but at the same time
introduces the presence of several unknown parameters. A key challenge faced in
this scenario is to determine the values of these unknown parameters against
known behavioral specifications. The solutions that have been presented so far
estimate the parameters of a given model against a single specification whereas
a correct model is expected to satisfy all the behavioral specifications when
instantiated with a single set of parameter values. We present a new method,
BioMETA, to address this problem such that a single set of parameter values
causes a parameterized stochastic biochemical model to satisfy all the given
probabilistic temporal logic behavioral specifications simultaneously. Our
method is based on combining a multiple hypothesis testing based statistical
model checking technique with simulated annealing search to look for a single
set of parameter values so that the given parameterized model satisfies
multiple probabilistic behavioral specifications. We study two stochastic
rule-based models of biochemical receptors, namely, Fc$\epsilon$RI and T-cell
as our benchmarks to evaluate the usefulness of the presented method. Our
experimental results successfully estimate $26$ parameters of Fc$\epsilon$RI
and $29$ parameters of T-cell receptor model against three probabilistic
temporal logic behavioral specifications each.
