COVID-19, BAYES’ RULE, AND SIMPSON’S PARADOX
https://mindmatters.ai/2021/09/covid-19-bayes-rule-and-simpsons-paradox/
This article mainly about the applications of Bayes’ Rule in COVID-19 vaccination and its effect. There were 58% of Israelis hospitalized for COVID-19 were fully vaccinated, it seems that vaccinations are useless for protect COVID-19. However, when we explore the data by Bayes’ Rule, it may is different from our intuition. There were 515 persons hospitalized for COVID-19, the probability of being fully vaccinated is 301/515 = 0.584. The probability hospitalized if not vaccinated is 214/1302912 = 0.00016425, while probability hospitalized if vaccinated is 301/5634634 = 0.00005342. The later is 3 times higher than not vaccinated. Also when we process data, the Simpson’s Paradox, which a trend appears in several groups of data but disappears or reverses when the groups are combined. In this example, the risk for the unvaccinated are 12.25 for people under the age of 50 and 6.76 for those over the age of 50, but only 3.07 for the entire population because the unvaccinated are not in proportion for younger and less vulnerable to COVID-19. The reality is that, young or old, the unvaccinated are much more likely to be hospitalized for COVID-19.
In our class or some statistics course, we learned about Bayes’ Rule. It tells us that most tests cannot have accurate of 100%, some tiny errors may cause huge bias when we estimating the result. However, the Bayes’ Rule gives us an accurate computation method that may different from out first intuition but very accurate. The Covid-19 is still issue in the world, without Bayes rules, it is very difficult to fight with the pandemic.