Hi Anastasia,
> In the Comparison with Empirical measurements part of the article
> the mean 95% confidence
> agnles are calculated for the three methods. However, I have
> trouble differentiating between the
> methods as it seems that four approaches are listed: DT model and
> MCMC, 35.4 partial volume
> model and MCMC, 36 and DT model with empirical measurements, and
> 33.9. Was the analysis
> done across the four approaches with pre-selected angle values?
> What was the rationale for these
> specific angle values?
>
There are not four, but three approaches that are compared there:
1. Fitting DT parameters using MCMC (i.e. having a probabilistic
model on the DT parameters)
-> this gives a posterior pdf on e.g. the principal eigenvector
2. Fitting the partial volume model using MCMC
-> this gives a posterior distribution on the local fibre orientation
3. Calculating the confidence interval on the DT principal
eigenvector using bootstrap
-> this is referred to as Jones' method
From each of these three methods, a 95% confidence angle was
extracted, the value of which (average across the brain) is 35.4 for
the first, 36 for the second, and 33.9 for the third. The point here
is that these values are similar, but the last method requires lots
of data (bootstrap) (and is not even ground truth), while the two
first only require one data set.
> In addition are the values of ceil (x), floor (x) normalized in
> any way to ensure that the values of
> the probability function g introduced in the Interpolation part of
> the article range from 0 to 1?
>
It is already "normalised". If you have a point (x,y,z) in continuous
coordinates, then the probability of choosing a point (x0,y0,z0) on
the grid for interpolation is:
p(x0,y0,z0|x,y,z) = p(x0|x)p(y0|y)p(z0|z) ---> independence of the
dimensions
and for each of the dimensions:
p(x0=floor(x)|x) = the formula in the paper
p(x0=ceil(x)|x) = 1-p(x0-floor(x)|x) ---> it is normalised!
p(x0=other) = 0
same for y0 and z0.
Cheers,
Saad.
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