Least Square pitfalls

[Michael Black]

I'd like to point out something to users of this software.

I was involved about 40 years ago with a national security project where we had a rather boisterous argument between a Naval Research Lab (NRL) scientist and a Pacific Northwest Lab (PNL) mathematician.    The NRL system had almost caused WWIII back in 1973 when it incorrectly identified a Russian ship as carrying nuclear weapons in the Mediterranean.  The US military had a world-wide yellow alert.  The NRL system used multiple-nonlinear-least-squares fitting on gamma spectroscopy.  The problem with the NRL system was it spit out "best fit" which, turns out, was wrong more often than not.  We confirmed that with field tests.

The NRL person was adamant his system was good...the PNL person called bullxxxx (literally) and proceeded to show that there was a rather large set of "best fits" when you did all possible  combinations and applied an F-Test for a cutoff.   There was a lot of yelling that went on as the NRL system had been around since the 1960's

So...what one has to do is this....

#1 Ensure your library contains all possible contributors -- this is where many are lacking as there are many cases where this involves everything in the world that could possibly contribute.

#2 One method that kind-of-works is  once you have a best fit you drop one element at a time and see how it affects the fit result.  What we found with the PNL software was any element that was in the set of all best fits was highly likely to actually be in the sample.

Doing all possible combinations is normally intractable and PNL had a program we used which, unfortunately, I didn't keep.  It used some math magic from a Russian paper to do all possible combinations quickly.

Mike Black

Retired USAF