🚀 go-pugleaf

I am far from expert in your particular problem, but you seem to be 
encountering a common problem in numerical analysis.  Perhaps my 
answer will trigger some other replies to your inquiry.

In article <0096060C.3C725B20@uinpla.npl.uiuc.edu> tayloe@uinpla.npl.uiuc.edu (Rex Tayloe) writes:
>

  [... details of actual thesis problem omitted ...]

>    1) Is anyone familiar with the method on p.308 of "Probability and
>Statistics in Particle Physics" by Frodesen et. al? (I dont know the proper
>name of the method).  It works well for most events using the LL hypothesis but
>fails for the LS hypothesis due to the fact that one of the matricies is very
>close to singular and cannot be inverted. What am I doing wrong?

If it is "close" to singular you should get an answer; the problem is with 
its reliability and the warning flags it should raise. 

There are two possible problems: your fit parameters in the LS case are 
not really independent of one another or you have encountered a standard 
problem with large least squares systems.  (A large least-squares matrix 
tends to resemble the Hilbert matrix, which has an inverse but has the 
property of being almost indeterminant when you try to solve it with 
any numerical method on machine with finite precision.)  Everything you 
say seems to argue against the latter problem, unless I missed something 
important.  A look at the error matrix might give some guidance. 

Your trouble with other methods might also be due to a correlation, 
since I gather you use the same description of the fit function in 
all cases.  

>    4) Are there guidelines for a reasonable covariance matrix? I find myself
>looking at the darn thing not being able to tell if it is right (other than the
>diagonal terms are the error**2). Should it be positive definite or something
>like that?  Mine always have a fairly large condition number (~10000-100000) Is
>this a signal of something wrong?

The off-diagonal entries are telling you about correlations in your fit.  If 
they are large, it is because you are trying to fit parameters that are not 
entirely independent of one another.  Your problem in (1) above would imply 
that such a result is likely.  If there is a single large off-diagonal 
entry, that is where your correlation lies.   

You might also try looking at the Chi-square surface in the space of such 
correlated parameters for guidance; a rotation to a better parameterization
could be all you need to get a fit. 

Hope this helps.

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)