Using Bayes’ Theorem to Consume News More Intelligently
This article discusses how Bayes’ Theorem can leveraged when making everyday decisions. Primarily, how it can be useful in simply updating our beliefs when presented with more evidence, or in determining whether an outcome is significantly more likely given some condition.
When examining Bayes’ Theorem, it can be helpful to breakdown the formula into terms of outcomes and conditions:
P(Outcome|Condition) = (P(Condition|Outcome) * P(Outcome)) / P(Condition)
In an example where you are weighing the probability that you have the flu, getting the flu would be considered the outcome while pieces of evidence such as results of a flu test would be considered conditions. In order to properly update your beliefs when presented with new information, three pieces of information are needed: the base rate of the outcome, the sensitivity of the evidence, and the specificity of the evidence. The base rate of the outcome can be defined as P(Outcome) which is also known as the prior probability. The sensitivity of the evidence can be described as P(Condition|Outcome) while the specificity can be defined as P(Condition|-Condition). With respect to aforementioned example, the base rate would be baseline probability of having the flu, the sensitivity would be the probability of receiving a positive flu test given you have the flu, and the specificity would be the probability of receiving a positive flu test given you do not have the flu. In order to for a condition to strongly influence the probability of an outcome, both a high sensitivity and specificity are needed.
This outcome/condition-based means of thinking of Bayes’ Theorem can be leveraged to logically digest additional news. Let’s consider an instance where the base rate is low: say, getting ALS. Since the probability of getting ALS is so slim, the posterior probability (the probability of getting ALS given a certain condition) will also likely be very low. For example, if a news organization released an article stating that “99% of people who eat fish do not get ALS”, you would understand that this statistic is not very useful since nearly 99% of all people do not get ALS regardless of whether they consume fish or not. Whereas, in a situation where the base rate is high (such as dying before the age of 100), the posterior probability (the probability of dying before the age of 100 given a certain condition) is likely very high as well. For example, if a news outlet stated that “95% of people who have been on an airplane die before the age of 100.”, you would understand that this is also not useful since most people die before 100 regardless of if they have ever flown on a plane. These concepts can be effectively leveraged in order to distinguish how significant certain new releases are.
Work Cited:
https://towardsdatascience.com/how-to-consume-news-more-intelligently-using-bayes-theorem-a3273d0fff5e
https://www.investopedia.com/terms/b/bayes-theorem.asp