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Bayes’ Theorem and False Alarms

http://allendowney.blogspot.com/2015/08/bayes-theorem-in-real-life.html

The attached article describes a situation regarding a carbon monoxide going off and the chances of it being a false alarm. Upon research, the author found that the chance of a false alarm is low, however the chance of a false alarm given a faulty detector is much higher. Then, the author gives more insight on other possibilities: fresh pavement on a nearby street, construction down the street, a smoldering fire inside a wall can all trigger the detector. These plausible situations again increase and decrease the likelihood of a false alarm, but the author felt more secure in the chances of a false alarm, but just to be sure, he called the fire department who then confirmed that there was no CO anywhere.

The situation this article depicts the usage of Bayesian probability. As more information is collected, the chances of certain outcomes change. This directly parallels the information cascade shown in the Majority Red/Blue model in past problem sets. The second person in line will make a different judgment than the 9th person who also knows what the 8th person knows. This situation also shows that a strictly Bayesian mindset doesn’t always work. The author couldn’t rule out the chances of a smoldering fire, and considered updating his information based on that, only to find that there was in fact no fire.

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