Dear Anastasia,
I’ve been looking at a lot of Tracula path.pd files and I’ve found that some probability distributions are only a single voxel wide, similar to the path.map file. The few none-zero voxels in these path.pd files have very high probability values. When an isosurface is generated for these tracts, it looks like a short thin blob somewhere in the usual tract distribution. I’ve seen descriptions in the archives of similar “short thin tracts,” but, from what I have seen, no one has offered a satisfying explanation for why these occur.
What I think is happening in these tracts is that a maximum-probability (or local maximum) path is found during a burn-in iteration and all following perturbations of that path are rejected. Since the probability value in the path.pd is equal to the number of sample paths intersecting that voxel, finding a local maximum early on results in a small number of very high-probability voxels. Consistent with this explanation, I’ve found that this issue occurs more frequently when nburnin is set to 1000 (default = 200). A similar issue can occur if a local maximum is found early during the sample iterations, and this results in a path.pd file containing a small number of voxels with very high values surrounded by a larger area of low-value voxels. When a 20% threshold is applied, the result is the same as when a local maximum occurs during a burn-in iteration.
Does my understanding of this issue seem correct?
None of this would be a problem if my only aim were to find the single path with the maximum a posteriori probability, but I’m concerned that the average and weighted_average sats for these tracts will be less accurate. Since these distributions include small fractions of the number of voxels included in most tract distributions, is it likely that the average and weighted_average stats from these narrow distributions are less representative of the whole tract and more subject to random noise?
Given these concerns, what type of overall path statistics do you think is most descriptive of a tract? Also, do you feel that higher nburnin and nsample values should lead to superior results? I would have thought this to be the case, but now it seems to me that setting either of these values too high will result in narrow probability distributions and bad statistics.
Thank you, Dillan