In that case, the probability that you want is the conditional
probability that "the path starting at A, passes through x and B,
knowing that A connects to B"
which, as you know, is: p(A->x->B | A->B) = p(A->x->B)/waytotal(A->B)
then in what I wrote below, you simply have to replace p(A->x->B) by
the conditioning on A and B being connected a priori.
You are right that the two events are not independent. Knowing that A-
>x->B does indeed tell you about A<-x<-B, but it is hard to say how
much it tells you!
Cheers,
Saad
On 1 Oct 2008, at 10:18, Andreas Bartsch wrote:
> Hi Saad,
>
>> assuming the two events are independent
> which they are certainly not, don't you think?
> Anyway, how about normalizing that output (i.e. the sum of the two
> fdt_path minus their product) to a meaningful waytotal? Would you
> have to simply have to add the two waytotals for that?
> Thanks, hope all is well!
> Cheers-
> Andreas
>
>
>
>
> -----Ursprüngliche Nachricht-----
> Von: FSL - FMRIB's Software Library im Auftrag von Saad Jbabdi
> Gesendet: Mi 01.10.2008 10:55
> An:
[log in to unmask]
> Betreff: Re: [FSL] probtrackx in MNI space
>
> Hi -
> It is important to keep in mind what is the probability that you want
> to calculate, it will tell you whether you want to add, substract,
> multiply or divide.
>
> Probtrackx calculates the probability that the path of least hindrance
> to diffusion from A passes through x: P(A->x). Using a waypoint B, the
> values become now the probability that the path of least hindrance to
> diffusion from A passes through x and B, i.e. p(A->x->B).
>
> Now combining p(A->x->B) and p(A<-x<-B), what you want is the
> probability that either the path from A to B or from B to A passes
> through x, which means:
>
> p( [A->x->B] or [A<-x<-B] ) = p( [A->x->B] ) + p( [A<-x<-B] ) -
> p( [A-
>> x->B] and [A<-x<-B] )
>
> Assuming the two events are independent (i.e. passing through x coming
> from A to B, or from B to A), the last probability is the product of
> both maps.
>
> So in order to calculate the probability that you want, you would need
> to add both maps, and substract their product.
>
> Cheers,
> Saad.
>
>
> On 30 Sep 2008, at 18:25, Cherif Sahyoun wrote:
>
>> Hi Markus,
>>
>> Matt and Saad will correct me if I'm wrong, but I'd say the way
>> you're proposing will cause you to lose any meaningful relationship
>> between the waytotal and your image. i.e. if you add, then
>> essentially the statement that waytotal is the total number of
>> streamlines that "made it" between your masks is preserved, but once
>> you multiply your images, then it would seem like your waytotal is
>> not as helpful...
>> (i like the idea of multiplying to get rid of outliers though...
>> i've been thresholding as per previous posts).
>>
>> Cherif.
>> ------------------------------------------------------------------------------------------
>> Cherif P. Sahyoun HST-
>> MEMP
>>
>> Developmental Neuroimaging of Cognitive Functions
>>
>> C: 617 688 8048
>> H: 617 424 6956
>>
[log in to unmask]
>>
>> "Live as if this were your last day. Learn as if you'll live forever"
>> Ghandi
>> -------------------------------------------------------------------------------------------
>>
>>
>> On Tue, Sep 30, 2008 at 3:41 AM, Markus Gschwind <
[log in to unmask]
>>> wrote:
>> Hi!
>> I am following your discussion with a lot of interest!
>> Here I have a question:
>> Why wouldn't you MULTIPLY (instead of add) the paths AB and BA?
>> I thought it is a more conservative measure of what is in common and
>> trancking outliers will dorp out. (And take the mean of waytotals).
>>
>> Thanks,
>> Markus
>
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Saad Jbabdi,
Postdoctoral Research Assistant,
Oxford University FMRIB Centre
FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
+44 (0) 1865 222545 (fax 222717)
[log in to unmask] http://www.fmrib.ox.ac.uk/~saad
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