  In this paper, we consider the well known problem of non-linear
identification of the rates of the reactions involved in cells with Monod
functions. In bioprocesses, generating data is very expensive and long and so
it is important to incorporate prior knowledge on the Monod kinetic parameters.
Bayesian estimation is an elegant estimation technique which deals with
parameter estimation with prior knowledge modeled as probability density
functions. However, we might not have an accurate knowledge of the kinetic
parameters such as interval bounds, especially for newly developed cell lines.
Hence, we consider the case when there is no accurate prior information on the
kinetic parameters except qualitative knowledge such that their non-negativity.
A log-Gaussian prior distribution is considered for the parameters and the mean
and variances of these distribution are tuned using the Expectation
Maximization algorithm. The algorithm requires to use Metropolis Hastings
within Gibbs sampling which can be computationally expensive. We develop a
novel variant of the Metropolis-Hastings within Gibbs sampling sampling scheme
in order to accelerate and improve on the hyperparameter tuning. We show that
it can give better modeling performances on a relatively large-scale simulation
example compared to available methods in the literature.
