The MAP method is based on the assumptions that:
- each region is relatively homogeneous in terms of ‘true’ signal;
- the amount of noise is reasonable;
- the number of voxels used to compute the inference is sufficient;
There are relevant details (with links to papers and simulations) in this link.
In your data, I can see that signal in the WM is close to zero (~0.005), so it is not surprising that, with a bit of noise, some tracts within the WM would be estimated below zero.
Now, when comparing these results to the BIN results, even though the BIN results are never negative (they cannot, as you show in the histogram), it does not imply that the BIN results are “more valid”. They could still be way off the true value because of partial volume effect.
To find out about the validity of the MAP method in your case, I would look at a few things. First, how homogeneous is the signal in the surrounding CSF? I’m asking this because the MAP uses priors from the mean GM, WM and CSF signal to regularize values. So, if the CSF signal is salt and pepper, then it will likely not be stable enough to use it as a prior, and in this case you should rather use the ML method, or maybe the WA (or BIN).