How to use Bayes rule in real world

1. Bayes Rule
Belief + Evidence -> Revise your Belief

2. Why should you care?
- Become smart(er)
- It was used for Treasure Hunt of $800Mn
- Know: How good is your manager, How bug free is ur code...
- Interpret a diagnosis test with 99% TP and 99% FP (Eg: Covid RT-PCR)
- Understand our scientific method (philosophy)
- Understand Monty Hall problem
- Use fancy phrases: Extraordinary claims require extraordinary evidence

3. Bayes Rule (the abstract math symbols)
P(H | E) = P(E | H) * P(H) / P(E)
We can make it more complex to confuse/scare...
P(H | E) = P(E | H) * P(H) / P(E | H) * P(H) + P(E | !H) * P(!H)
H:Hypothesis; E: Evidence

4. Lets do better by stating it in plain english...
When you see evidence;
Update your belief
This is sthg you should; Tatoo it in your brain - 3Blue1Brown
Sidenote: Levels of understanding:
- What is it?
- Why is it true?
- When is it useful?

5. Simplified (and useful) version
Odds * Strength of evidence = new Odds
Technically,
Prior Odds * Relative likelihoods = Posterior Odds

7. Why is it so hard to apply? Becoz its simple :)

8. How good are interviews?
Let us assume that 1 out 10 developers are good
and some observation on interviews:
● How many good developers clear interviews? (8 out of 10)
● Also ask: How many bad developers clear interviews? (1 out of 50)
New Belief: 1:10 * (8/10 : 1/50) = 1:10 * 40:1 = 4:1
i.e., 4/(4+1) is the probability you found a good candidate, post interview
Insight: Its very hard to improve ur process, instead filter/screen better

9. How good is the manager?
Let us assume that 1 out 10 managers are bad
and some observations: he does bad code reviews, is micromanaging you
● How many bad managers do this? (8 out of 10)
● Also ask: How many good managers do this? (1 out of 20)
New Belief: 1:10 * (8/10 : 1/20) = 1:10 * 16:1 = 16:10
i.e., 16/(16+10) is probability of your manager is bad

10. Monty hall
You select Door 1, Monty chooses Door 3
Prior = 1:1:1
Relative Likelihood = ½:1:0
Posterior = ½ :1:0 = 1:2:0
so, Switch -- probability is ⅔ vs ⅓
Note: Bayes rule in this form is superior to P(E|H)*P(H)/P(E)

11. What the heck is Likelihood?

12. Credits/Links
https://arbital.com/p/bayes_rule/
Betterexplained
3blue1brown https://www.youtube.com/watch?v=HZGCoVF3YvM&t=620s