CHICOS Maximum Likelihood Code

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Write-up

Reconstruction errors are generated by Minuit MIGRAD code. It seems there is an "ErrorDef" which needs to be set. It defaults to 1 which is the appropriate value for a chi-square fit, but it should be set to 0.5 for a likelihood fit. Documentation also suggests using MINOS to get better errors. This was in the code but commented out.

Testing:
- version 303: Same as previous
- version 303A: Set ErrorDef to 0.5
- version 303B: Uncommented call to MINOS

Version 303 vs Version 242 (raw data)

X Error
X Error (zoom in) <- Likelihood errors are smaller.
Y Error
Y Error (zoom in)
Theta Error
Phi Error
LogE Error

Version 303A vs Version 303 (raw data)

X Error
X Error (zoom in) <- Setting ErrorDef makes likelihood errors smaller.
Y Error
Y Error (zoom in)
Theta Error
Phi Error
LogE Error

Version 303B vs Version 303A (raw data)

X Error
X Error (zoom in) <- Using MINOS has little effect.
Y Error
Y Error (zoom in)
Theta Error
Phi Error
LogE Error

Checking how the energy errors relate to the energy of the shower:

Version 242
Version 303

Version 303 looks more reasonable.

Going to keep the ErrorDef change but remove the call to MINOS, as it is a performance hit.