ctools

• dll_sigstep: Determines the step size in standard deviations for generating the profile
• dll_sigmax: Determines the maximum number of standard deviations away from the best fit flux value to profile the likelihood

• e2dnde_scan: Values at which the likelihood profile was evaluated at
• loglike: Reference log-likelihood for the associated loglike profile in this energy bin
• dloglike_scan: delta log-likelihood profiles relative to the associated value in loglike and evaluated at fluxes in e2dnde_scan

• If the normalization has a non-zero error and that error is smaller than the normalization itself, then logarithmically spaced bins are generated covering the range of fluxes specified by [-dll_sigmax,dll_sigmax]
• Otherwise, the range covers [10 ^-24 ,10 ^-14 ] or [log10(norm), 10 ^-14], whichever is larger. The reason for covering such a large range is to ensure there is sufficient coverage to interpolate the loglike value when plotting the profile. This range was also chosen to encompass the flux range covered by a 0.01x → 10x Crab strength source in the range 0.1-100 TeV. There’s no restriction in format guide on the number of bins in a profile, or even that all profiles in an SED need to have the same number of bins, so we can change this if needed.

	method=SLICE	method=NODES
Strong Source
Weak Source

There is an open question regarding when 'method=NODES’ is used. In this case the reference loglike value is the log-likelihood for the entire energy range, rather than just the energy range of the given bin. The profiles are still valid, but the value represented in the 'loglike’ column is defined differently than when 'method=SLICE’ is used.

• Energy → e_ref
• ed_Energy → e_min
• eu_Energy → e_max
• Flux → e2dnde
• e_Flux → e2dnde_err
• TS → ts (lowercase)
• Npred → npred
• UpperLimit → e2dnde_ul

• SED_TYPE ('likelihood’ if likelihood profile is generated, otherwise 'e2dnde’)
• UL_CONF (Confidence level of the upper limits, extracted from the default value of ctulimit since csspec does not support setting this value)

1. Decide whether we want to leave the difference in definition of loglike column for the two methods
2. Decide if we want to keep the breaking change of renaming the columns

• User: jcardenzana
• Repo: ctools
• Branch: 2938_loglike_profile

I’ve implemented the code as per the gamma-astro data format. This required some re-structuring of the header keywords in order to make them as consistent as possible between the version that includes the likelihood profiles and the version that does not. The headers are now as follows:

• e_ref → Reference energy (TeV)
• e_min → Energy bin lower bound (TeV)
• e_max → Energy bin upper bound (TeV)
• ref_dnde → Differential Flux at `e_ref` (counts/MeV/cm2/s)
• ref_e2dnde → Differential flux at `e_ref` (erg/cm2/s)
• ref_npred → Predicted number of events (counts)
• norm → Normalization factor for bin (unit-less)
• norm_err → Relative error for bin (unit-less)
• norm_ul → Relative upper limit for bin (unit-less)
• ts → Test statistic for best fit spectrum

• norm_scan → normalized flux values for the flux profiled likelihood (similar to norm column)
• loglike → Log likelihood at reference flux
• dloglike → Log likelihood profile at associated norm_scan

• 'SED_TYPE’ = 'norm,dnde,e2dnde,npred’ identifies that the norm representation (not likelihood) is being used and that ref_dnde, ref_e2dnde, and ref_npred are present in the file.
• 'SED_TYPE’ = 'likelihood,dnde,e2dnde,npred’ identifies that the file contains all the same columns as the 'norm’ version, but with additional columns containing the likelihood profiles.

The test scripts and fits file have been updated to reflect the changes in the keywords and column names.

After testing the code, I now have the following SED plots generated by csspec and plotted with show_spectrum.py. Short story is that the 'SLICES’ method appears to generate profiles that look just fine, but the NODES function has some issues when there is very little data in a bin:

	method=SLICE	method=NODES
Strong Source
Weak Source

Basically, what appears to be happening is that the likelihood profile changes very rapidly (e.g. it drops several orders of magnitude between two interpolated flux bins) in these bins and the resulting interpolated profile appears as though it just cuts off.

Regarding the weak nodes image, if we zoom in to the region where the dominant number of flux points lie we get the following:

Looking more closely at the second bin shows that there are actually points where the delta-loglike goes positive, which I don’t think should happen if we’ve found the best fit value in the initial fit. I’m a little unsure how to proceed from here, so any feedback would be appreciated.

• User: jcardenzana
• Repo: ctools
• Branch: 2938_loglike_profile

After a little more investigation, I believe the issue that I was seeing had to do with the amount of data that I was simulating. I increased to simulating 2 hours and the results that come out look much better (i.e. the profiles appear to line up with the spectral points which all appear within a reasonable differential flux range):

	method=SLICE	method=NODES
Strong Source
Weak Source

I’ve also added a brief tutorial demonstrating how to run csspec to generate the likelihood profiles and modified the documentation to reflect this.

• User: jcardenzana
• Repo: ctools
• Branch: 2938_loglike_profile

Merged into devel.