Bayesian rule: better decision making

This week I finished the Elements of AI -courses. I decided to write a blog post about things I learned, but I wanted to pick exactly one most important thing I learned. This would be the Bayesian rule that allows you to adjust your expectations on new evidence.

People are notoriously bad at incorporating new evidence when it comes to probabilities. For an example, consider AI-detection. Whenever AI-detector gives a positive, it is considered an evidence that the text was written by AI. However there's a problem: The detectors are inaccurate and also give false positives, and a perfect detector cannot be built. The problem is twofold: Authors do not publish their accuracy readings, and users ignore the problem of accuracy alltogether.

Consider that an AI-detector gives 80% of time a positive reading for AI-written text, and 20% of time it gives a positive reading for human-written text. We can take a ratio 0.8/0.2 = 4, then multiply it with odds. Consider your existing belief of odds, how many of the texts are likely written by AI?

0:1 >>> 0:1
1:1 >>> 4:1
2:1 >>> 8:1

If you believe none was written by AI, perhaps because you sourced the text from an archive before there was AI, then you should use the first odds. If it's impossible that AI was used, then AI-detector positive means nothing.

If you believe that it's 50:50, or 1:1. There's one text against every human-written text. Then 1 in 5 texts detected to be written by AI, are actually written by human.

If you believe that 2 in 3 texts are written by AI, then the likelihood that AI-detected text is actually written by AI is 8 to 1. That is. 8 in 9 texts detected positive are actually written by AI.

Lot of Bayesian rule has been written, so this blogpost is not exactly a tutorial on Bayes. Though, it's worthwhile to tell it can be represented in both odds and probabilities. Both are important to understand.

More people should know about Bayes' rule

Understanding Bayes rule allows doing more informed decisions by updating our beliefs as new data becomes available. This is why more people should know about Bayes' rule:

  1. Improved decision making: Bayes' Rule can help make better decisions by incorporating new evidence into decision-making processes.
  2. Interdisciplinary applications: Familiarity with the concept can help people better understand the work of many fields, such as medicine, finance, artificial intelligence, psychology, etc.
  3. Encouraging critical thinking: Understanding Bayes' rule can help develop critical thinking skills and deeper appreciation for the importance of evidence and uncertainty in decision-making.
  4. Addressing cognitive biases: Familiarity with Bayes' rule can help recognize and mitigate cognitive biases such as confirmation bias, by emphasizing the importance of incorporating new evidence into their beliefs.

So if you haven't learned Bayes' rule yet, consider giving it a new try.

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