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

On Mon, Jun 07, 2004 at 10:59 -0400, Nat Butler wrote:
> > > 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)


It is possible that there is a bug for the case when only two
parameters are variable.

If you repeat this test using the pileup.sl test case
distributed with isis (which has 3 variable parameters) you can
see that the other parameters are indeed varied:

> isis -n pileup.sl
testing pileup....  Parameters[Variable] = 6[3]
            Data bins = 1024
           Chi-square = 979.2
   Reduced chi-square = 0.9591
ok

Welcome to ISIS Version 1.2.1
Copyright (C) 1998-2004 Massachusetts Institute of Technology

isis> list_par;
cutoff_plaw(1)
 idx  param             tie-to  freeze         value         min         max
  1  cutoff_plaw(1).norm    0     0            0.005           0        0.01  
  2  cutoff_plaw(1).alpha   0     0                1           0           3  
  3  pileup<1>.nregions     0     1                1           1          10  
  4  pileup<1>.g0           0     1                1           0           1  
  5  pileup<1>.alpha        0     0              0.5           0           1  
  6  pileup<1>.psffrac      0     1                1           0           1  
isis> vconf(2);
Best fit par[2]=  1.00000000e+00: stat= 9.79226434e+02
Minimizing for par[2]=  5.00000000e-01
chisqr= 8.3427e+05:
 cutoff_plaw(1).norm=  1.99915301e-04 pileup<1>.alpha=  1.72948129e-01

delta-chisqr =  7.0254e+05   accept =  1.5368e+02
chisqr= 7.6727e+05:
 cutoff_plaw(1).norm=  1.81295106e-04 pileup<1>.alpha=  8.14723686e-01

delta-chisqr =  6.7009e+04   accept =  8.3427e+01
chisqr= 7.4281e+05:
 cutoff_plaw(1).norm=  1.83038639e-04 pileup<1>.alpha=  9.05791937e-01

delta-chisqr =  2.4459e+04   accept =  7.6727e+01
chisqr= 8.8921e+05:
 cutoff_plaw(1).norm=  1.83329085e-04 pileup<1>.alpha=  1.26986816e-01

chisqr= 7.3966e+05:
 cutoff_plaw(1).norm=  1.83443300e-04 pileup<1>.alpha=  9.13375856e-01

..



I'll fix this for the next release.

Thanks,
-John

-- 
John C. Houck         MIT Center for Space Research
tel: 617-253-3849           77 Massachusetts Avenue
fax: 617-253-8084          Cambridge, MA 02139-4307
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