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Comment by NhanH | Hacker News Reader

Everyday passing by is a sample day that you can use to estimate the risks. Even if you argue that terrorism is a relatively new risk in the past few decades and start your sampling from September 2001, we still have more than a decade of sample days to estimate the risk. That's a huge sample.

There might not be enough sample to know how many people would be harmed during a terrorist attack. But there is definitely enough information to estimate the risk of an attack itself.

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Actuary here. I don't have the math at my fingertips, but to confidently estimate the risk of any occurrence you need a significant sample of the event, not just a significant amount of exposure.

So for instance, if you are estimating the mortality rate of a 25 year old and the rate for an 85 year old you would be equally confident in each estimate if your data sample contained an equal amount of deaths for each, not an equal amount of life-years.

So while we have many days of exposure to terrorism risk, we do not have many occurrences and therefore do not have a confident estimate of the rate of major terror attacks.

Definitely not an actuary here so forgive my ignorance: Isn't the fact that 'we do not have many occurrences' by itself enough to establish a lower bound?

You mean upper bound -- being a more likely killer than heart attacks is a statistical impossibility. Same for car accidents. Same for iron deficiency, Trypanosomiasis, and a bunch of other things.

Hm, no I really meant 'lower bound', as in 'we have seen x events in y days to date, so there can't be fewer than that'. And then you'd have to adjust that as more evidence rolls in.

Not an unreasonable conclusion, but let's say there is a true (hidden/unknowable) rate of deaths X. You'd expect, not knowing the statistical distribution, maybe half the time the measurement (adding deaths from events) it'll be less and half the time it'd be more, just like any other random variable measurement. So it isn't a lower bound, just a fantastic guess that's bound to be pretty close. How close will it be? Well, the sample size is pretty low, so honestly it could be quite wrong. This is what the mega-parent was saying.

edit: you can get a lower bound, from a statistical perspective, the same way, where you go out a couple standard deviations to make up for small sample size, e.g. terrorism is more dangerous than being hit by two meteors at the same time, but if you wanted to make the case terrorism is more dangerous than something strange like water overdose that's probably true but not a lower-bound level statistical certainty.

A I see (or at least, I think I see), it's just another bell curve and this is the center line of that curve?

It's a single data point on the curve, so probably close to average, but yeah, that's the notion.

Thank you for the explanation!

Right, risk estimation would be a probability distribution by itself. It won't be a five sigma confidence in the estimation. But if one was to do the work and actually calculate the estimation distribution, I'd find it hard to believe that the result would be much of any concern than our normal daily risk.

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