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Re: (meteorobs) Doomsday Icarus
On Fri, 13 Mar 1998, Wayne T Hally wrote:
> That does leave a major question though..dot since the original pass by
> distance (sorry I'll use miles here...the point is the same) was to be 30,
> 000 +/- 180,000 miles. The new one is 600,000 miles (I have seen no error
> bars on this so far). We still need to explain how 30,000 + 180,000 (I
> think that makes 210,000) became 600,000. In other words, the error on the
> first orbit does not include where the revised number comes out. So why
> were the error bars not large enough??
There are two points here.
1) +/- is one standard deviation, i.e. approximately 68 per cent of
the time the value will lie between +210,000 and -150,000. It does
not mean that the value only lies between these two values. The
probability drops off as you move away from the estimated perigee. A
perigee of 600,000 is only a three-standard-deviation event. So it is
possible, albeit unlikely at somewhat less than 1 per cent.
2) There are formal/internal and systematic/external errors. Given
the original data, the formal/internal error budget based upon the
data then to hand was +/- 180,000. However, as is usually the case,
the systematic errors (because the data are insufficient or biased, or
you make invalid assumptions) are often much larger. A classic case
is the determination of the Hubble parameter. Sandage would quote a
formal error of say 50+/-2 km/s/Mpc, but given other results, the true
error is much larger because of systematic uncertainties and biases.
Malcolm
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