Integrating Bayesian Analysis and Cumulative Probability Generates High Confidence Using a Single Microbial Source...

Microbial source tracking can identify waterbodies at risk of contamination using host-associated molecular markers. No assay used for microbial source tracking is both 100% host-specific and sensitive for human or animal fecal contamination. Using literature sensitivity and specificity values, Bayes' Theorem for conditional probability was applied to the human fecal-associated HF183 marker in a microbial source tracking context. Type I and Type II error rates were examined across a range of priors. Conditional probabilities were investigated using two human-associated markers, HF183 and HumM2, concurrently. Cumulative probability analysis was used to explore the likelihood of true contaminant detection using multiple samples. Probability of human fecal contamination was calculated for all combinations of positive and negative marker results given three samples. Results demonstrate the respective influence that specificity and sensitivity values exert on the likelihood of true positive and true negative. Using practical priors, high levels of confidence (99%) in results were observed when HF183 and HumM2 were used concurrently. Cumulative probability analyses showed that multiple samples from a single location can provide a >95% level of confidence in positive and negative results, suggesting that when multiple samples are necessary to account for in situ variability, a single marker can yield sufficiently reliable results.