Re: {MPML} Monte Carlo uncertainty estimation

David Tholen

4) Statistical Ranging. This is really the only reliable means of
computing orbits with very short arcs, ranging from a few minutes to a
few days. This approach is also Monte Carlo in style, but it randomly
samples two observations from the available set and selects two random
topocentric distances at the observation times. From two obs and two
distances you get an orbit, and that's your Virtual Asteroid. There are
a host of variations on this method: You can also add noise to your
sampled observations if you like. Dave Tholen and Rob Whiteley, working
independently from Virtanen et al., have implemented a method that fits
an orbit to all the available observations with the topocentric distance
constraints applied. Or something like that.

Statistical ranging _will_ reveal alternate solutions and will give
robust uncertainty regions, which in some cases can be really wild looking.
A good question is whether our technique can be accurately described as
being Monte Carlo in style. I've always associated randomness with the
term. When I add noise to a set of observations, I generate random
numbers, so that approach would certainly qualify for the term Monte
Carlo. However, KNOBS does not use any random numbers at all. It's
a methodical grid search, originally constrained by the hyperbolic
limit (and one can apply a prograde constraint as well). As more
observations are acquired, the constraint comes from statistics, but
the topocentric distance and radial velocity are still taken from a
grid of values rather than from generating random numbers over a
specified range. What do you think, does it still qualify as being
Monte Carlo in style?

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