Thanks for your reply. If the data is approximately Gaussian but with a
longer tail, is it likely that the (pseudo) max t-distribution is wider
(or has a longer tail) than a true max t-distribution that is generated
from Gaussian data?
/Anders
Roberto Viviani skrev 2010-11-02 08:56:
> Hi Anders,
>
> your data cannot be Gaussian and have a much longer tail. The longer
> tail means that they are not Gaussian. Your result tell me one of the
> following
>
> 1) your data depart so much from normality that parametric results are
> not applicable. The Bonferroni too depends on significance values
> computed parametrically.
>
> 2) your implementation of the permutation test is wrong, or your
> implementation of the Bonferroni correction is wrong.
>
> Best wishes,
> Roberto
>
>
>
>
>> Hello, I do not apply any second level analysis since I only work with
>> single subject fMRI. I have implemented a random permutation test to
>> calculate a threshold, but I get higher thresholds than Bonferroni
>> correction and random field theory. The residuals look Gaussian
>> distributed but have a much longer tail, does this make sense to you?
>>
>> /Anders
>>
>> Roberto Viviani skrev 2010-11-01 14:59:
>>>> Good point, I mean that the MRI observations have Rician-distributed
>>>> noise. My question however remains, is this considered in SPM or is it
>>>> assumed that the noise is Gaussian?
>>>
>>> There is no single distribution that holds for all MRI data used in
>>> practice. Voxel-based morphometry data, for example, are
>>> probability values bounded between 0 and 1. Other data are ratios
>>> of random variables.
>>>
>>> There are two distributional issues to consider in general:
>>> marginal (the distribution of the data seen voxel by voxel) and
>>> joint (viewed multivariately). In the SPM approach, the first
>>> affects the marginal distribution of the parametric map, the second
>>> the exactness of the correction for multiple comparisons.
>>>
>>> In general, the marginal distribution may not be the same over the
>>> volume. So it isn't very useful to think of it as just one
>>> distribution. But anyway the parametric map will marginally tend to
>>> normality for large samples, as those commonly found in functional
>>> MRI. So for fMRI/EPI, I would not worry much about distributional
>>> issues arising from the EPI signal. Besides, 'EPI-specific noise'
>>> has a limited influence on the distribution of residuals at the
>>> second level, which is where you carry out inference. Instead, the
>>> dominant source of variance arises from the subject-to-subject
>>> variation of the effect of interest.
>>>
>>> The sensitivity of the test to violations of distributional
>>> assumptions depends on the test statistic. Voxelwise corrections
>>> (which use the maximum over the volume as test statistic) are
>>> quite sensitive to marginal violations, and much less to joint
>>> distributional violations. In contrast, cluster-level corrections
>>> (using the maximum cluster size) are very sensitive to violations
>>> of the joint distributional assumption.
>>>
>>> There is a simple way to correct for marginal volations: rank the
>>> data voxel by voxel, and carry out a permutation test. The issue of
>>> corrections for joint distributional assumptions is a topic of
>>> active research.
>>>
>>> Best wishes,
>>> Roberto Viviani
>>>
>>>
>>>>
>>>> /Anders
>>>>
>>>> 2010-10-31 10:19, Gael Varoquaux skrev:
>>>>> On Sat, Oct 30, 2010 at 07:45:07PM +0200, Anders Eklund wrote:
>>>>>
>>>>>> An interesting discussion, do you know if SPM uses the fact that the
>>>>>> noise in MRI is Rician distributed and not Gaussian distributed?
>>>>>>
>>>>> Forgive me for asking a naive question, but is the noise in fMRI
>>>>> really
>>>>> Rician-distributed? The MRI-observation noise is
>>>>> Rician-distributed. I
>>>>> believe that this comes directly from the measurement process.
>>>>> However,
>>>>> with EPI, there are much more processes contributing to 'noise' than
>>>>> imaging noise, such as residual movement or vascular and respiratory
>>>>> noise.
>>>>>
>>>>> I am not even sure that the EPI-specific noise (such as
>>>>> field-inhomogeneity fluctuations that can clearly be seen in the
>>>>> ventricles) are Rician-distributed. If someone on the mailing-list
>>>>> who
>>>>> understands the physics behind the EPI noise could enlight me, I'd be
>>>>> much obliged.
>>>>>
>>>>> Gael
>>>>>
>>>>
>>>> --
>>>> --
>>>> -----------------------------------------------------------------------
>>>>
>>>>
>>>> Anders Eklund
>>>> Phd student
>>>>
>>>> Medical Informatics, Department of Biomedical Engineering
>>>> CMIV, Center for Medical Image Science and Visualization
>>>>
>>>> Tel: +46 73 6003790 mail: [log in to unmask]
>>>> Fax: +46 13 101902 web: http://www.wanderineconsulting.com/
>>>> -----------------------------------------------------------------------
>>>>
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