Maximum Ignorance Probability: What do you do when you must estimate a probability and there is ZERO information? Surgeon did 60 operations & 0 failure. What's the failure rate? I realized the trick wasn't in the literature when someone wrote a paper in SPL on my blog post.

There was a great paper from Kaplan and Garrick in the late 70s applied to transport of hazardous nuclear waste and the actuaries’ collective inability to price the risk because a rail disaster hadn’t happened yet! Similar method

Thanks a million!

When I worked for a defense contractor in the late 70s/early ' 80s this approach was a common way engineers evaluated systems’ reliability with limited information.

Laplace’s rule gives me 1/62, and then I'd approx halve that again so approx round number 1/100. Saw it here on Laplace rule limitations

Concise and elegant. The probability can also be updated with new information (for example if the surgeon had 20 more operations and still got 0 failure)

this book profiles similar scenarios (Bayesian Statistics)

You still have your prior and that is free to choose. A good one might be the average failure rate of all surgeons. If your prior is unreasonable, the peer review will point that out.

The max-entropy distribution for p is uniform over [0,1]. Using this as a Bayesian prior, we get a probability of 1/(1 + 61) = 1/62 ≈ 1.61% of mortality for the thoracic surgeon's next surgery, which is higher than Taleb's number. Unexpected for the author of The Black Swan 😉. I get this same answer again if I assume that * for each surgery there are K possible detailed conditions, * i of these lead to mortality, and * 0 <= i <= K, but i is otherwise unknown, and then simply use a counting argument applying the classical definition of probability, taking the limit as K goes to infinity. This argument assumes that the detailed conditions are sufficiently detailed that they determine mortality.

Slides hard to follow, but it's a concept worth deepening

Sir, what do you think about Bitcoin? I’m just kidding LOOOOOOOL