Re: Behavior for conf() different from XSPEC (bug?)

> > I've noticed that the conf() function in ISIS (and fconf() and vconf())
> > determine parameter confidence intervals by freezing the other parameters
> > and by varying the interesting parameter until a desired dchi^2 is
> > achieved.  
> 
> That's not the way it works -- what makes you think so?
> You can use vconf to see how all non-frozen parameters 
> are varied during the confidence limit search.

I just checked vconf() on a couple of spectra on my linux box here.  I'm
running isis-1.1.6.

I was fitting power-laws in both cases.  I found the best fit model and
then calculated the confidence interval using vconf().  For both cases,
it's clear that vconf is not minimizing the other parameters.  Here's one
case:

best fit model:
powerlaw(1)
 idx  param             tie-to  freeze         value         min         max
  1  powerlaw(1).norm       0     0          22.2139           0       1e+10  
  2  powerlaw(1).PhoIndex   0     0          2.31315          -2           9  

then:
isis> vconf(2)
Best fit par[2]=  2.31315001e+00: stat= 6.21836779e+01
Minimizing for par[2]=  1.56575004e-01
par[2]=  1.56575004e-01  stat=  2.3452e+08  dstat=  2.3452e+08
Minimizing for par[2]=  2.31291818e+00
par[2]=  2.31291818e+00  stat=  6.2184e+01  dstat= -4.0274e-05
Minimizing for par[2]=  2.31291816e+00
par[2]=  2.31291816e+00  stat=  6.2184e+01  dstat= -4.0274e-05
Minimizing for par[2]=  2.31291813e+00
par[2]=  2.31291813e+00  stat=  6.2184e+01  dstat= -4.0274e-05
Minimizing for par[2]=  1.23474657e+00
par[2]=  1.23474657e+00  stat=  1.9622e+04  dstat=  1.9560e+04
Minimizing for par[2]=  1.77383235e+00
par[2]=  1.77383235e+00  stat=  4.7419e+02  dstat=  4.1200e+02
Minimizing for par[2]=  2.04337524e+00
par[2]=  2.04337524e+00  stat=  1.0486e+02  dstat=  4.2681e+01
Minimizing for par[2]=  2.17814669e+00
par[2]=  2.17814669e+00  stat=  6.9518e+01  dstat=  7.3343e+00
Minimizing for par[2]=  2.24553241e+00
par[2]=  2.24553241e+00  stat=  6.3722e+01  dstat=  1.5383e+00
Minimizing for par[2]=  2.23191003e+00
par[2]=  2.23191003e+00  stat=  6.4486e+01  dstat=  2.3027e+00
Minimizing for par[2]=  2.22755809e+00
par[2]=  2.22755809e+00  stat=  6.4769e+01  dstat=  2.5857e+00
Minimizing for par[2]=  2.20285239e+00
par[2]=  2.20285239e+00  stat=  6.6768e+01  dstat=  4.5840e+00
Minimizing for par[2]=  2.22602102e+00
par[2]=  2.22602102e+00  stat=  6.4874e+01  dstat=  2.6903e+00
Minimizing for par[2]=  2.22578012e+00
par[2]=  2.22578012e+00  stat=  6.4891e+01  dstat=  2.7069e+00
Minimizing for par[2]=  2.22574278e+00
par[2]=  2.22574278e+00  stat=  6.4893e+01  dstat=  2.7095e+00
limit found:  2.22574278e+00  dstat=  2.7095e+00
Minimizing for par[2]=  2.48796447e+00
par[2]=  2.48796447e+00  stat=  6.8176e+01  dstat=  5.9927e+00
Minimizing for par[2]=  2.43070750e+00
par[2]=  2.43070750e+00  stat=  6.5256e+01  dstat=  3.0723e+00
Minimizing for par[2]=  2.41684346e+00
par[2]=  2.41684346e+00  stat=  6.4651e+01  dstat=  2.4669e+00
Minimizing for par[2]=  2.42241063e+00
par[2]=  2.42241063e+00  stat=  6.4888e+01  dstat=  2.7043e+00
Minimizing for par[2]=  2.42253934e+00
par[2]=  2.42253934e+00  stat=  6.4894e+01  dstat=  2.7099e+00
limit found:  2.42253934e+00  dstat=  2.7099e+00
2.42254
2.22574

If I plug 2.42254 into the above model and do eval_counts, I get:
Chi-square = 64.89, which is what vconf() reported.  If I fit the
normalization paramater with the index frozen to this value, I get:
Chi-square = 62.81 .

So, the real 90% confidence interval is broader.  Apparently, vconf()
has not varied the normalization parameter.  This also happens on my
linux box at home.  It also happens running version 1.1.8 on the Sun's
at CSR.

-Nat
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