alt Hacker News> we should default to the calculation of 2-4x the rate.
No we should not. We should accept that we don't have any statistically meaningful number at all, since we only have a single incident.
Let's assume we roll a standard die once and it shows a six. Statistically, we only expect a six in one sixth of the cases. But we already got one on a single roll! Concluding Waymo vehicles hit 2 to 4 times as many children as human drivers is like concluding the die in the example is six times as likely to show a six as a fair die.
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NewJazz • yesterday at 10:46 PM
Uh, the miles driven is like rolling the die, not hitting kids.
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More data would certainly be better, but it's not as bad as you suggest -- the large number of miles driven till first incident does tell us something statistically meaningful about the incident rate per mile driven. If we view the data as a large sample of miles driven, each with some observed number of incidents, then what we have is "merely" an extremely skewed distribution. I can confidently say that, if you pick any sane family of distributions to model this, then after fitting just this "single" data point, the model will report that P(MTTF < one hundredth of the observed number of miles driven so far) is negligible. This would hold even if there were zero incidents so far.