Bayes’ Rule environmental applications
https://www.accessscience.com/content/applications-of-bayes-theorem-for-predicting-environmental-damage/YB100249
This article details the use of Bayes’ rule to predict and model how certain changes impact the natural environment in a specific region. Bayes’ theorem is used in predictive modeling via naive Bayes’ classifiers. This classifier predicts the probability an event happens givens some observed evidence. It is derived as follows. Bayes’ theorem states that the probability of an event occurring, given observed evidence is equal to the evidence observed, given the event occurring, we get the observed evidence times the probability of the observed evidence, divided by the probability of the event occurring. The naive Bayes’ naive assumption is that each feature in our evidence matrix is pairwise independent to all of the other features, and that each feature is equally important. While this assumptions seems a bit unreasonable, in practice, the naive Bayes’ classifier works fairly well. In addition, it has the advantage of having a very short runtime.
The applications of this model are very interesting. Firstly, this model is used in the article to predict how a newly implemented stormwater management system affects water quality in a region. To do this, researchers first calculated the probability distribution of how much sediment is removed by the stormwater management system. They did this by collecting data experimentally and fitting a distribution to that data. We can then use this as the likelihood of the stormwater management system impacting the water quality, since redirected sediment impacts water. We then use our collected data on past water quality as our prior distribution and then apply Bayes’ theorem to predict the effect.
In addition, Bayes’ theorem is also used to predict how bacteria from sewage treatment plants effect an ecosystem. From previous experimentation, it was found that the spread of bacteria generally follows a log-normal distribution. Using this probability distribution combined with Bayes’ rule, we can predict. The likelihood of bacteria contaminating a water source and the animals in it.
This article relates to what we are learning in class because it is an interesting application of Bayes theorem. It has real life impacts in predicting environmental effects. The most interesting thing about this article is that it uses Bayes rule in an unaltered form, so it shows how what we learned in class has direct applications.