April 29, 2017
Thomas Bayes
Dear Mr. Bayes,
I am writing this letter to thank you for coming up with the Bayes Theorem. It uses logic and evidence to understand and update our knowledge. We can revise our belief with new data, and we have been doing that for centuries now. You have provided the formal probability rules to combine data with prior knowledge to get more precise understanding. This way of thinking is inherent in our decision making now. I have benefitted so much from this rule. I cannot thank you enough for this.
Today, I want to share a story with you about how Joe, the curious kid used Bayes Theorem to impress his boss.
Joe works part time at the MARKET.
His usual daily routine is to receive the bags of apples from Andy’s distribution company (A) and Betsy’s distribution company (B), check for quality and report to his boss.
One day, during this routine, he stepped out of the loading dock to check his twitter feed.
When he returned, he noticed that there was a bad apple → a rotten bag of apples in 100 bags of apples.
Since the bags were identical, he could not say whether the bad apple was from Andy’s or Betsy’s. All he knew was that Andy’s was contracted to deliver 60 bags and Betsy’s was contracted for 40 bags.
Joe is a sharp kid. Although he did not see who delivered that bad apple, he knew he could assign a probability that it came from Andy’s or Betsy’s. He called me for some advice.
Mr. Bayes, I hope my students are calculating the updated probability of getting a problem on Normal Distribution in the mid-term based on the review session. Your discovery saw the light after the invention of Monte Carlo approaches. Bayesian methods are widely applied now. You can rest assured in the heaven. Your posterity has ensured the use of Bayes Theorem for centuries to come, albeit making it a methodological fad sometimes.
Sincerely,
A posterior Bayesian from Earth
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But there’s no heaven for Mr. Bayes or anyone else. He’ll never know the full impact he’s made on civilization.