[tsimionescu]

Note that this is equivalent to saying "there's no way to know". This guess doesn't give any insight, it's just the function that happens to minimize the total expected error for an unknowable duration.

Edit: I should add that, more specifically, this is a property of the uniform distribution, it applies to any event for which EndsAfter(t) is uniformly distributed over all t > 0.

[froobius]

I'm not sure about that. Is it not sometimes useful for decision making, when you don't have any insight as to how long a thing will be? It's better than just saying "I don't know".

[tsimionescu]

Not really, unless you care about something like "when I look back at my career, I don't want to have had a bias to underestimating nor overestimating outages". That's all this logic gives you: for every time you underestimate a crisis, you'll be equally likely to overestimate a different crisis. I don't think this is in any way actually useful.

Also, the worse thing you can get from this logic is to think that it is actually most likely that the future duration equals the past duration. This is very much false, and it can mislead you if you think it's true. In fact, with no other insight, all future durations are equally likely for any particular event.

The better thing to do is to get some even-specific knowledge, rather than trying to reason from a priori logic. That will easily beat this method of estimation.

[froobius]

You've added some useful context, but I think you're downplaying it's use. It's non-obvious, and in many cases better than just saying "we don't know". For example, if some company's server has been down for an hour, and you don't know anything more, it would be reasonable to say to your boss: "I'll look into it, but without knowing more about it, stastically we have a 50% chance of it being back up in an hour".

> The better thing to do is to get some even-specific knowledge, rather than trying to reason from a priori logic

True, and all the posts above have acknowledged this.

[tsimionescu]

> "I'll look into it, but without knowing more about it, stastically we have a 50% chance of it being back up in an hour"

This is exactly what I don't think is right. This particular outage has the same a priori chance of being back in 20 minutes, in one hour, in 30 hours, in two weeks, etc.

[froobius]

Ah, that's not correct... That explains why you think it's "trite", (which it isn't).

The distribution is uniform before you get the measurement of time taken already. But once you get that measurement, it's no longer uniform. There's a decaying curve whose shape is defined by the time taken so far. Such that the statement above is correct, and the estimate `time_left=time_so_far` is useful.

[tsimionescu]

Can you suggest some mathematical reasoning that would apply?

If P(1 more minute | 1 minute so far) = x, then why would P(1 more minute | 2 minutes so far) < x?

Of course, P(it will last for 2 minutes total | 2 minutes elapsed) = 0, but that can only increase the probabilities of any subsequent duration, not decrease them.