Discrepancy in probability/chi^2

[ryanlevy]

Reported by Manuel Zingl and Khaldoon Ghanem (thanks both!) there are some potential subtle problems with definitions. The code seems to use Q=chi^2 / Ndat - alpha*S in the minimization routine rather than the reported Q=1/2chi^2 - alpha*S

Current options:

• Use the Ndat version of Q and fix Q and chi2 functions in the code
  • we should test how things will change under this
• Remove the (re)scaling
  • this seems to reasonably match e.g. MEM for the Bryan method

[jpfleblanc]

So what you think is most correct. Would be nice to see the impact of this on the example test cases as a minimum.

[ryanlevy]

case1.pdf
case2.pdf
case3.pdf

Khaldoon graciously provided three test cases along with their outputs from MEM i.e. Jarrell Code.
to be more explicit:

• Original Code is the current release
• Patched (1/2chi^2) is Khaldoon's proposed patch which removes the extra 2/ndat on lines 89 and 99 of maxent_helper.cpp
• Patched (chi^2/ndat) carries through the extra factor of 2/ndat to the objective function Q so its consistent everywhere (changing the Q function )

[egull]

This looks remarkably clean. I'm ok with changing the convention.