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Comment by YeGoblynQueenne | Hacker News Reader

So, according to this rule, if I wait for 10 minutes for a bus to come and none does, and then I wait for another 10 minutes for an alien invasion and none happens, the two have the same upper bound on their probability?

Or are we going to start talking about priors, on buses and alien invasions, in which case the rule of three is not really useful? If I want to know how likely a specific book is to have typos, can't I just go look for statistics on typoes in books, and won't that give me a better estimate than a "rule" that will give the same results no matter what it is that it's trying to model?

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This is the scenario where you know nothing else other than you waited 10 minutes for this event and it didn't happen.

Sure, if you have more data, then you can get much tighter bounds for your estimate.

This is the scenario where you know nothing else other than you waited 10 minutes

To make the math work, I think you need to make several other assumptions. Don't you also have to know that that ten minutes you sampled are representative? That the events (if they did occur) are independent? It seems odd that you'd in a situation where you can rely on specific assumptions like these while also believing that buses and aliens are equally likely to appear.

You always have more data -background knowledge- unless you've only existed in those last 10 minutes.

And if something has really never happened before, like my alien invasion example, what have we learned by applying the rule of three?

Honestly- perform the experiment yourself. Wait for X time, then calculate 3/X. Do you now have an upper bound on the probability that an alien invasion will happen?

>Wait for X time, then calculate 3/X. Do you now have an upper bound on the probability that an alien invasion will happen?

Assuming we would observe an alien invasion and write about it, we have about 5000 years since humans started writing. So 3/5000a, so an upper bound on an alien invasion in a year (assuming p hasn't changed since we started writing) is 0,06% per year.

It's an upper bound in any case, meaning that is this or less. That includes p = 0. You're just 95% confident that it won't be higher than that.

But maybe the aliens brought us our writing system.

Yes, I do have a reasonable (95% confidence, as per article) upper bound on the probability - as I haven't noticed an alien invasion during my lifetime, it seems reasonable to conclude that noticeable alien invasions are very rare events and happen less frequently than once every decade. Possibly much less frequently, possibly many orders of magnitude less frequently, possibly never, but that's how upper bounds work.

An upper bound of "maybe, who knows" is not useful or informative enough to make a whole "rule" about it.

>the two have the same upper bound on their probability? Using only that information, yes. Replace the names of the two events with "event A" and "event B" and it doesn't sound so weird.

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