Bayes’s theorem and bias
http://www.theguardian.com/science/life-and-physics/2014/sep/28/belief-bias-and-bayes
When one thinks about probability and statistics, it makes sense to associate these topics of study with hard numbers, facts, or conclusions made on actual collected data. While it can admittedly be very easy to misinterpret or misrepresent certain data sets, probability and statistics still base themselves on the scientific method. In class, we have discussed the ideas of conditional probability and Bayes’ Rule specifically in terms of how we can use these tools to build mathematical models for how information cascades occur. The relevance can be seen in asking questions like, “What is the probability that this is the better class to take given the CourseRank reviews I’ve read and the number of students already enrolled in each one?” Or, “What is the probability that this jar of M&M’s is majority red, given the M&M I just drew and the guesses I’ve heard?” For the most part, conditional probabilities and Bayes’ Rule are used in reasoning and decision-making. However, what should be clear and based on numbers also has the possibility of being clouded by bias and emotion.
The article linked above explores the notion that Bayesian statistics actually introduces a certain level of subjectivity into the scientific process — but “subjectivity” and “science” aren’t words that should be closely connected to each other. Some scientists have deemed this subjectiveness as unacceptable when navigating in the realm of probability and statistics, being that tests and evidence should lead to objective conclusions. But apparently, with human nature, this subjectivity is inevitable in collecting data and creating conclusions based on Bayesian statistics. According to the article, Bayes’ rule acknowledges that even if you have well collected evidence, the impact it has on your beliefs still depends on your prior assessment of the theories involved. If one’s “epistemological interpretations” of the given data associated with a certain end result do not agree with this result, then in his or her mind the probability does not have much meaning. We can look at this through the example of climate change. If you are strongly against technology, machinery, and the general goal of modernizing simple life processes, then you will place a higher probability on carbon dioxide emissions eventually dooming everyone. On the other hand, if you are bothered by the zeal of environmental activists and the earth-loving nature of hippies, then you will place a much lower weight on mounting evidence of human-caused global warming. Despite this article’s arguments, which definitely have their merit in how people will always interpret data however they want, Bayes’ rule still serves as a good tool for decision-making under uncertainty.