Bayesian statistical inference is applied to the process model parameter estimation. It is expected that the Bayesian inference framework provides a way to properly handle the nonlinearity of the process models. Posterior probability distribution of the estimated parameters is computed by quasi-Monte Carlo (QMC) simulation of the likelihood function. Maximum a posteriori (MAP) or marginal posterior mode (MPM) estimate of the model parameters is identified that is believed to be more robust than the maximum likelihood estimate (MLE), especially under circumstances where the number of experiments or data points are limited. The confidence region that is evaluated by the proposed method would not necessarily be ellipsoidal as is, however, the case with the conventional or "conservative" Cramer-Rao lower bounds (CRLB) that are calculated by approximation or linearization of the Fisher information matrixes (FIM). It is shown that the "correlation" among some of the estimated parameters can be explained by the "singularity" that is inherent to the model assumed for the investigation. The MPM estimate, in particular, of each parameter can be computed even under such (partially) singular model situations.