Bayes in Carbon Monoxide Alarms
Many events in life are better predicted when provided with evidence. These types of events follow Bayesian logic, updating the probability of a hypothesis as more information becomes available. We can break down these events, mathematically, using Bayes’ Theorem.
Take a low-level, household example such as your Carbon Monoxide alarm going off. Carbon Monoxide is undetectable by human senses. Therefore, it is easy to doubt the validity of such alarms, especially when you cannot hear, see, or smell Carbon Monoxide. If your alarm goes off, is there really Carbon Monoxide present or is your system malfunctioning? Bayes Theorem actually allows us to calculate the probability that the alarm was false, given that it went off by this formula:
P(false alarm | alarm went off) = p(false alarm) p(alarm went off | false alarm) / p(false alarm) p (alarm went off | false alarm) + p(true alarm) p (alarm went off | true alarm)
Although this probability would likely turn out extremely small if we plugged in the actual values, there is constantly technology developing that aims to make this Bayesian probability even smaller. For example, The Nest Protect Smoke & Carbon Monoxide alarm, minimizes the potential for false alarms. Not only does it detect if Carbon Monoxide is present, it can actually tell if and how long the chemical has been building up in your home. Additionally, it can provide information as to where the leak is coming from. The addition of information with this technology (rather than the simple yes/no of the outdated Carbon Monoxide alarm) makes the probability of false alarm even more minute, according to Bayes’ Theorem.
There will always be errors in technology that will translate to uncertainties in validity. Larger households require multiple Nest systems to accurately detect a presence of Carbon Monoxide. How much is enough? Will we ever have 100% certainty of alarms? Likely not.