CHICOS Maximum Likelihood Code

Hit/Nohit function

If the observed intensity is > 10, the intensity probability function is now 1-e^(-expected intensity). This solved the problem with large hits. Only 02-03-07 does not reconstruct.
Shower parameters
Shower parameters, no accidentals

Timing Probability function

In investigating the contributions to the likelihood, I noticed that P_TDF was sometimes greater than 1. This is because the TDF is normalized to 1. What is really wanted is the integral from t-delta to t+delta of the TDF. I put this in the code with delta = 50 ns. Now all -Log(likelihood) contributions are positive.

Because the TDF gets very flat far from the center of the shower, I had to put in a cutoff: currently P_TDF is limited to be no less than 0.001. Finally all showers reconstruct!
Shower parameters
Shower parameters, no accidentals

Previously corrected errors in 3.00 code

All previously corrected errors in the 3.00 code were propagated to 3.01 and newer versions. This includes error bars, data display, and LatDist CE/CM errors. The low LDF was originally solved by changing P_TDF from I*TDF to Poisson(I,I*TDF). I changed the probability back to P_TDF=TDF, but I'm investigating this a little more.

There was also a page noting that looping site-by-site doubled the energy of the showers. However it appears to no longer be the case that going site-by-site makes any difference.

Plots of shower energies using the most recent code:

Above 10^18 eV, the max likelihood fits are lower than the chi-square fits, but below 10^18 eV, they are higher.

Test showers:

I don't think the energy is off by a factor of 2, but it is low sometimes. I think maybe the times are being fit well at the expense of the intensity.

One can do a dummy reconstruction and observe that in some cases raising the energy makes the likelihood worse even though it makes the chisquare value better. Perhaps the unhit sites are contributing too much?