conditional vs joint probabilities

At computer-vision-meets-astronomy we discussed Fadely's image-patch modeling system, and how to use it for calibration. We had a long discussion about the following issue: If you have a patch that is a good fit to the model except in one pixel (where, maybe, calibration parameters are wrong), should you look for that badness of fit in the total joint likelihood of all the pixels or in the conditional likelihood of the one pixel given the others? Intuitions diverged; in principle there is one joint PDF that contains all the information, so it doesn't matter. But that ignores the point that the PDF we have fit is not in any sense accurate! So we reduced scope to a very simple functional test of this point.

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