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Are these maximum likelihood targets the normal maximum likelihood function or the minus one?
We are using the maximum likelihood targets described here: Lunin, V.Y., Afonine, P.V. & Urzhumtsev, A. (2002). Acta Cryst. A58, 270-282. Lunin, V.Y. & Skovoroda, T.P. (1995). Acta Cryst. A51, 880-887.
Should I expect an increase or decrease of the target?
Decrease. But see below...
If the part of the restraints is not combined with the x-ray part, the target is showing is not the actual target the program is trying to maximize or minimize.
Yes, that's right.
The values don't have a trend, at least I can't see a trend in my log file.
The x-ray target may go up since we refine x-ray target + geometry target. The total will always go down (that's how the minimizer works), but an individual contribution may go up a bit. Ralf