A hybrid Bayesian–neural network approach for probabilistic modeling of bacterial growth/no-growth interface

A hybrid probabilistic modeling approach that integrates artificial neural networks (ANNs) with statistical Bayesian conditional probability estimation is proposed. The suggested approach benefits from the power of ANNs as highly flexible nonlinear mapping paradigms, and the Bayesʹ theorem for computing probabilities of bacterial growth with the aid of Parzenʹs probability distribution function estimators derived for growth and no-growth (G/NG) states. The proposed modeling approach produces models that can predict the probability of growth of targeted microorganism as affected by a set of parameters pertaining to extrinsic factors and operating conditions. The models also can be used to define the probabilistic boundary (interface) between growth and no-growth, and as such can define and predict the values of critical parameters required to keep a desired pre-specified bacterial growth risk in check. A modular system incorporating the various computational modules was constructed to illustrate the application of the hybrid approach to the probabilistic modeling of growth of pathogenic Escherichia coli strain as affected by temperature and water activity. The proposed approach was compared to other techniques including the traditional linear and nonlinear logistic regression. Results indicated that the hybrid approach outperforms the other approaches in its accuracy as well as flexibility to extract the implicit interrelationships between the various parameters. Advantages and limitations of the approach were also discussed and compared to those of other techniques.