Bayes’ Theorem and Predictive Models for Pollution
In class we learned about Bayes’ Rule and as a probability measure for uncertainty and its applications in the Herding experiment, where people guess whether the urn contains majority red or blue balls. We have also observed, through forming this mathematical model, that people’s decision eventually comes to a consensus as they are influenced by the crowd’s behavior, and an information cascade begins to occur. Interestingly, a similar process can be applied as well when it comes to monitoring the environment.
An interesting article from the National Exposure Research Laboratory suggests that statistical modeling techniques such as the Bayes’ theorem can be used in conjunction with prior beliefs of events. Including metrics such as sedimentation in stormwater infrastructure systems, to predicting water quality conditions of particular water body. Which can then in turn determine the suitability of the body of water for potential use, and help decide whether it is drinking-grade, or should be left for recreation or agriculture use. This is a very immediate problem because often times, pollutant concentrations are difficult and often expensive to measure directly.
This article by Gronewold et al. introduces the application of Bayes’ Theorem to solve water pollution problems. One of the example figure they showed in the article represented the fraction of sedimentation as θ, which is the random variable/parameter as conditioned on a fixed x, which is the mass of pollutant removed by a certain management infrastructure. Using Bayes’ theorem, this quantity is then proportion to the product of the prior probability distribution and a likelihood, which is a function modeling sediment removed rates derived from samples from another study site. Interestingly, the calculation they performed does not include a denominator from Bayes’ rule with the probability of the event conditioned upon, as the paper explains that it would yield a ratio constant.
Another interesting approach mentioned was that this method can similarly be applied to help predict fecal coliform concentrations: which is a germ found in digestive tracts of farm animals and wildlife, in bodies of water in a site in eastern North Carolina where people tend to harvest shellfish This can be practical to guide predictions about likelihood of violations of standards with bacteria with harvested shellfish which could be deemed a threat for human and the surrounding ecosystem. For instance, if these Bayes’ model predicts a fecal coliform concentration of greater than 14 organisms per 100ml (which is approximately the 90th percentile), local fisheries can then manage the harm by closing off these harvesting areas and putting up warning signs.
Reference:
Gronewold, Andrew D., and Daniel A. Vallero. “Applications of Bayes’ Theorem for Predicting Environmental Damage.” AccessScience, McGraw-Hill Education, 2010.
(URL: https://www.accessscience.com/content/applications-of-bayes-theorem-for-predicting-environmental-damage/YB100249#YB100249s003)