Hi Michael - Even if it starts very close to the true max of the
distribution, in practice it'll never stay put. MCMC will accept a new
sample path with probability 1 if the new sample has greater probability
than the previous sample, and it will also accept it with some very small
probability if it doesn't. This means that it'll still explore the space
around the max, even if it ends up returning to the max pretty quickly. So
most likely there's something weird about the initial path if it doesn't
move at all.
Best,
a.y
On Tue, 23 Aug 2016, Harms, Michael wrote:
Hi Anastasia,
My interpretation of the “reinit” parameter is that it is for situations
where a narrow probability distribution is assumed to be incorrect. But
how do you know whether it is indeed incorrect, or whether in fact the
true equilibrium distribution is (correctly) very narrow?
In particular, my understanding of MCMC is that higher burn-in, and more
sampling iterations are only a “good” thing. i.e., If we have the time
and compute resources, we shouldn’t hesitate to increase them from their
defaults, to help to make sure we are capturing the true equilibrium
distribution. So, if increasing the nburnin and nsample values makes it
more likely to find spatially narrow tract distributions, isn’t that a
sign that the true distribution should indeed be narrow?
thanks,
-MH
--
Michael Harms, Ph.D.
-----------------------------------------------------------
Conte Center for the Neuroscience of Mental Disorders
Washington University School of Medicine
Department of Psychiatry, Box 8134
660 South Euclid Ave.Tel: 314-747-6173
St. Louis, MO 63110Email: mha...@wustl.edu
On 8/23/16, 4:44 PM, "freesurfer-boun...@nmr.mgh.harvard.edu on behalf of
Anastasia Yendiki" <freesurfer-boun...@nmr.mgh.harvard.edu on behalf of
ayend...@nmr.mgh.harvard.edu> wrote:
Hi Dillan - There's a work-around for this, see the reinit variable at the
bottom of the sample config file:
http://surfer.nmr.mgh.harvard.edu/fswiki/dmrirc
I'm hoping to make this happen automatically soon!
Best,
a.y
On Tue, 23 Aug 2016, Newbold, Dillan wrote:
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
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