How rational investors revise forecast/expectation using bayes rule

Can someone give me an example with some numbers as to how a investors would revise forecasts/expectation in a finance situation using bayes rule in a real life case. A simple example with numbers would be really helpfull. thanks

This isn’t finance related but its how i memorised this for the exam.

Let’s say 100 people decide to quit smoking (I quit about a month before L3).

  • 40% (40) begin their attempt at t=0 feeling confident they will succeed

  • 30% (30) end up being successful at t=1

  • Out of the 30% (30) that are successful, 83% (25) of these felt confident at t=0.

so the question is, what is the chance of success for someone that begins at t=0 feeling confident?

the answer is: 25 / 40 = 63% (i.e. much higher than the 30% chance we would give someone if we didn’t know whether or not they are confident).

Bayes formula is a fancy way of getting to the same answer: P(B|A) = (83% / 40%) * 30% = 63%

Hope this helps.


Many thanks for you help!