Calibration of the survival of salmonella bacterium to radiation using bayesian procedures

Calibration of food irradiation (i.e. foodborne bacterial pathogen control) uses data from a calibration experiment. This data consists of pairs (x_i, y_i) where x_i are the doses (kGy) at which the chicken meat is irradiated and y, are the corresponding bacteria populations (log CFU/g), where CFU stands for colony forming units. In order to describe the relationship between dose and population reduction the Student t-distribution is used to describe the predictive and calibrative densities:

By using Bayes theorem and incorporating a uniform prior distribution, the expression for the posterior density is obtained. Integrating the product of the likelihood of a new observation and the posterior density yields the predictive density. The predictive density acts like a new likelihood in the subsequent derivation of the calibrative density.

By incorporating a uniform prior distribution, the relationship between the calibrative and predictive density is simplified. The calibrative density describes the uncertainty of a new unknown dose x_n given a specific bacteria population y_n and the calibration data set z = (x, y). This type of analysis provides a quantitative description of the uncertainty about the dose. In addition, this approach allows factors such as temperature and atmosphere to be analyzed qualitatively. The effect of these factors on the resistance of Salmonella to radiation is examined. The Bayesian approach is used in the analysis of two research experiments.