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Subject:

Re: Bayesian Inference

From:

Will Penny <[log in to unmask]>

Reply-To:

Will Penny <[log in to unmask]>

Date:

Fri, 4 Jun 2004 12:20:27 +0100

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (573 lines)

Florentin Preoteasa wrote:

> Dear Sir,
>
> Thank you very much for all your help.
> Please excuse for bothering you with bayesian stuffs.
> Please be so kind and answer me to a question that my supervisor
> strongly advised me to put it :
> Why is wrong to use a conjunction for bayesian by selecting two
> contrasts for PPMs like selecting two contrasts for classical inference
> by pressing the shift button, if the software allows it and didn t ask for
> orthogonality?


Its not wrong. Its just that SPM2 can't handle making the contrasts
independent *if* they need to be made independent.

This is due to a bug in line 172 of spm_FcUtil.m which should read:

if ~(varargin{3}=='F'|varargin{3}=='T'|varargin{3}=='P'),


- in the release version of SPM2 the last clause is missing.

So for your data it must be the case that the contrasts don't
need to be made independent (the contrasts [1 0] and [0 1]
are orthogonal so if the errors are independent - i guess you must
have specified them to be independent by declining
to model 'non-sphericity' - then the contrasts will be independent).

Therefore everything is fine !

As a sanity check you should look to see that your results
are the same as those gotten using the IMCALC approach (which they
should be assuming you've used the same thresholds).

Sorry this has been so involved but, as far as I know,
you are the first to use Bayesian conjunctions.

Very best wishes,

Will.


> Please allow me to send you the map that we obtained for bayesian by
> conjunction.
> Thank you very much and your help is highly appreciated.
>
> Best wishes.
>
> Florentin Preoteasa
>
>
>
>> From: Will Penny <[log in to unmask]>
>> To: Florentin Preoteasa <[log in to unmask]>
>> CC: [log in to unmask]
>> Subject: Re: Bayesian Inference
>> Date: Thu, 03 Jun 2004 11:39:55 +0100
>>
>>
>>
>> Florentin Preoteasa wrote:
>>
>>> Dear Sir,
>>>
>>> Thank you very much for all your help. It is very kind of you.
>>> So after I did ANOVA and contrasts [1 0] and [0 1], and Bayesian and
>>> then the conjunction, I worked with imcalc.
>>> I took the PPMs and I made a AND operation as you described.
>>> I used the overlays   section function and I could compare the Bayesian
>>> conjunction with the image that I obtained from imcalc. Surprisingly
>>> we obtain the same pattern.
>>> Now the problem is if it is better to use Bayesian conjunction or
>>> imcalc.
>>
>>
>>
>> At the moment you *can* only use imcalc.
>>
>>> If imcalc is better please tell me how can I put the image (obtained
>>> by imcalc) on a render and what is the possibility to extract the
>>> coordinates of the voxels.
>>
>>
>>
>> In the SPM2 distribution under /toolbox/display_slices
>> are some functions that will help you to do overlays.
>> I don't know about rendering.
>>
>> In SPM - if you use 'DISPLAY' to show the images you can navigate
>> using the mouse
>> and the corresponding voxel/MNI co-ordinate will be displayed.
>> Alternatively you can type in a co-ordinate and SPM will move the
>> cursor there
>> and tell you what the value is.
>>
>> Best wishes,
>>
>> Will.
>>
>>
>>> Thank you very much for your help.
>>>
>>> Best wishes,
>>>
>>> Florentin Preoteasa
>>>
>>>
>>>
>>>> From: Will Penny <[log in to unmask]>
>>>> To: Florentin Preoteasa <[log in to unmask]>
>>>> CC: [log in to unmask]
>>>> Subject: Re: Bayesian Inference
>>>> Date: Wed, 02 Jun 2004 17:01:43 +0100
>>>>
>>>>
>>>>
>>>> Florentin Preoteasa wrote:
>>>>
>>>>> Dear Sir,
>>>>>
>>>>> Thank you very much for all your replies.
>>>>> I made a two condition model : ANOVA.
>>>>> I choose  two  groups, one group for a condition, and the same
>>>>> group for the other condition.
>>>>> I made the contrast [1 0] and [0 1]. These contrasts gave me the
>>>>> activations for each group.
>>>>> Then I did a Bayesian estimation, and again two contrasts [1 0] and
>>>>> [0 1].
>>>>> These contrasts were not orthogonal and I succeed to do a
>>>>> conjunction between them (in the same manner how you explained to
>>>>> me for classical inference).
>>>>
>>>>
>>>>
>>>>
>>>> Your resulting inferences are then conditional on the assumption that
>>>> the responses to the conditions are uncorrelated (this is a stronger
>>>> requirement than orthogonality - because the errors may be non-IID -
>>>> see `help spm_getSPM').
>>>>
>>>> It is possible to relax this assumption for the classsical inference.
>>>> In fact SPM automatically does this by adjusting the second contrast
>>>> so that it
>>>> is independent of the first.
>>>>
>>>> With Bayesian inference the selection of multiple contrasts
>>>> or more specifically, the automatic adjustment to enforce
>>>> independence, is *not
>>>> currently working* in SPM2. I will fix this and notify the list.
>>>> So if you've successfully managed to get Bayesian conjunctions working
>>>> in this way, your contrasts must already be independent.
>>>>
>>>> The other way to do Bayesian conjunctions is to assume
>>>> the conjunctions are independent and use IMCALC as previously
>>>> described.
>>>>
>>>>
>>>>> Then we made a conjunction in the classical way. What is
>>>>> interesting, is that this conjunction  is similar with a bayesian
>>>>> conjunction between these contrasts.
>>>>> But we found, that Bayesian conjunction responds better to our
>>>>> questions.
>>>>> What do you think ?
>>>>
>>>>
>>>>
>>>>
>>>> Well done !
>>>>
>>>>
>>>>> Thank you very for all your help.
>>>>>
>>>>
>>>>
>>>>
>>>> Another difference between the Bayesian conjunction
>>>> and the classical conjunction is that the Bayesian inference
>>>> gives regions that  (probably) have activations larger than
>>>> a particular (user specified) effect size(s). Whereas the classical
>>>> inference
>>>> looks at the ratio of effect size to effect variability
>>>> and shows those regions where the probability of no effect (for both
>>>> contrasts) is smaller than a (specified) level eg. 0.05.
>>>>
>>>> Best wishes,
>>>>
>>>> Will.
>>>>
>>>>
>>>>> Best regards,
>>>>> Florentin Preoteasa
>>>>>
>>>>>
>>>>>
>>>>>> From: Will Penny <[log in to unmask]>
>>>>>> To: Florentin Preoteasa <[log in to unmask]>
>>>>>> Subject: Re: Bayesian Inference
>>>>>> Date: Tue, 25 May 2004 15:14:53 +0100
>>>>>>
>>>>>>
>>>>>>
>>>>>> Florentin Preoteasa wrote:
>>>>>>
>>>>>>> Thank you very much for your reply.
>>>>>>> I have the PPMs now.
>>>>>>> My supervisor is not agree with imcalc.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>> Is it OK to make conjunction of them for commonalties?
>>>>>>> Thank you very much.
>>>>>>>
>>>>>>
>>>>>>
>>>>>> As long as the two PPMs are based on orthogonal contrasts then
>>>>>> the IMCALC scheme described below should be valid. At present this
>>>>>> is the only way to do a Bayesian conjunction analysis.
>>>>>>
>>>>>> If your supervisor is unhappy with this you should find out what
>>>>>> his/her objections are. Maybe its the 'Bayesian' aspect. If so you
>>>>>> could do
>>>>>> the same analysis using a classical conjunction inference, also as
>>>>>> described below.
>>>>>>
>>>>>> If its the 'conjunction' aspect your supervisor is unhappy with you
>>>>>> could try a masking approach. Use one contrast as an explicit mask
>>>>>> for the other.
>>>>>>
>>>>>> Best wishes,
>>>>>>
>>>>>> Will.
>>>>>>
>>>>>>> Best regards,
>>>>>>>
>>>>>>> Florentin Preoteasa
>>>>>>>
>>>>>>>> From: Will Penny <[log in to unmask]>
>>>>>>>> To: Florentin Preoteasa <[log in to unmask]>
>>>>>>>> CC: [log in to unmask]
>>>>>>>> Subject: Re: Bayesian Inference
>>>>>>>> Date: Tue, 25 May 2004 11:40:30 +0100
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Florentin Preoteasa wrote:
>>>>>>>>
>>>>>>>>> Dear Sir,
>>>>>>>>>
>>>>>>>>> Please I really need as soon as possible a response from you.
>>>>>>>>> I made the analysis as you suggest with imcalc.
>>>>>>>>> The only problem is that I don t have really a PPM map, with all the
>>>>>>>>> activations, and coordinates and so on. Because of that my
>>>>>>>>> supervisor does not agree the results with imcalc.
>>>>>>>>> It is OK to make a second level model (as two-sample t-test or
>>>>>>>>> ANOVA), to construct two PPMs for the two conditions ([10] and
>>>>>>>>> [01]) and then to make a conjunction between this contrasts in
>>>>>>>>> order to have the commonalties ?
>>>>>>>>> Thank you very much.
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> So, you don't have PPMs ?
>>>>>>>> If you don't have them then you certainly can't make
>>>>>>>> conjunctions of them.
>>>>>>>>
>>>>>>>> Maybe your supervisor is suggesting you do classical inference
>>>>>>>> rather than Bayesian inference. In this case, in the contrast
>>>>>>>> manager,
>>>>>>>> you select the two-contrasts you want to make a conjunction of
>>>>>>>> (to select the
>>>>>>>> second one hold down the shift key - (or shift and control -
>>>>>>>> can;t remember)). SPM
>>>>>>>> will then make a classical inference about the conjunction.
>>>>>>>>
>>>>>>>> Very best wishes,
>>>>>>>>
>>>>>>>> Will.
>>>>>>>>
>>>>>>>>
>>>>>>>>> Best regards,
>>>>>>>>> Florentin Preoteasa
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> From: Will Penny <[log in to unmask]>
>>>>>>>>>> To: Florentin Preoteasa <[log in to unmask]>
>>>>>>>>>> CC: [log in to unmask]
>>>>>>>>>> Subject: Re: Bayesian Inference
>>>>>>>>>> Date: Mon, 10 May 2004 13:14:39 +0100
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Florentin Preoteasa wrote:
>>>>>>>>>>
>>>>>>>>>>> Thank you very much for your replying.
>>>>>>>>>>> I never used imcalc and I do not know what should be enter
>>>>>>>>>>> when he askes the function to evaluate. Can you please advise
>>>>>>>>>>> me on that issue?
>>>>>>>>>>> Thank you very much.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> 1. Press imcalc.
>>>>>>>>>> 2. Images to work on: select the two PPM images.
>>>>>>>>>>
>>>>>>>>>> SPM refers to these as i1 and i2
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> 3. o/p filename ?
>>>>>>>>>>
>>>>>>>>>> type in eg. 'conjunction'
>>>>>>>>>>
>>>>>>>>>> 4. output function : i1 & i2
>>>>>>>>>>
>>>>>>>>>> The resulting image then has 1's when both thresholds
>>>>>>>>>> are met (see below) and zeros otherwise.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> For another condition, I have 9 controls for one condition
>>>>>>>>>>> and the same 9 for another condition and I want to see what
>>>>>>>>>>> is common for two conditions. Is it allright if I put all in
>>>>>>>>>>> a paired t-test and then I make the PPMs?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I don't think the paired test is appropriate here, because
>>>>>>>>>> that's for
>>>>>>>>>> detecting differences rather than commonalities.
>>>>>>>>>>
>>>>>>>>>> I'd just use a two condition model (eg. two sample t-test) and
>>>>>>>>>> then
>>>>>>>>>> get two PPMs - one for the [1 0] contrast and the other for [0
>>>>>>>>>> 1] - then
>>>>>>>>>> follow the strategy outline below (an above).
>>>>>>>>>>
>>>>>>>>>> Best, Will.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>> Thank you very much.
>>>>>>>>>>>
>>>>>>>>>>> Best regards,
>>>>>>>>>>> Florentin Preoteasa
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>> From: Will Penny <[log in to unmask]>
>>>>>>>>>>>> To: Florentin Preoteasa <[log in to unmask]>,
>>>>>>>>>>>> [log in to unmask]
>>>>>>>>>>>> Subject: Re: Bayesian Inference
>>>>>>>>>>>> Date: Wed, 21 Apr 2004 15:30:27 +0100
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Florentin Preoteasa wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Dear Sir,
>>>>>>>>>>>>>
>>>>>>>>>>>>> Please excuse me that I write directly to your e-mail, and
>>>>>>>>>>>>> not in mailing list of SPM. This because I do not have
>>>>>>>>>>>>> really a problem, just an advise, please.
>>>>>>>>>>>>> I saw your papers related to Bayesian inference. I
>>>>>>>>>>>>> understood that most important thing is that one who use
>>>>>>>>>>>>> that will not have multiple comparison problems.
>>>>>>>>>>>>> Please tell me is correct for me to find by Bayesian
>>>>>>>>>>>>> inference the commonalties between two groups (controls and
>>>>>>>>>>>>> patients), each group with 9 subjects?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> I think the best way to do this would be to create two
>>>>>>>>>>>> posterior
>>>>>>>>>>>> probability maps (PPMs), one for each effect, and then use
>>>>>>>>>>>> imcalc to do
>>>>>>>>>>>> an AND operation. Voxels that survive this process satisfy
>>>>>>>>>>>>
>>>>>>>>>>>> [p(control effect > g) > 0.95] & [p(patient effect > g) > 0.95]
>>>>>>>>>>>>
>>>>>>>>>>>> where g is your effect size threshold (this specifies what
>>>>>>>>>>>> an activation is
>>>>>>>>>>>> eg. an effect larger than 0.5% of the global mean) and 0.95
>>>>>>>>>>>> is your
>>>>>>>>>>>> probability threshold (this controls the certainty in your
>>>>>>>>>>>> inference).
>>>>>>>>>>>>
>>>>>>>>>>>> Best, Will.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>> Thank you very much.
>>>>>>>>>>>>> Best regards,
>>>>>>>>>>>>>
>>>>>>>>>>>>> Florentin Preoteasa
>>>>>>>>>>>>>
>>>>>>>>>>>>> _________________________________________________________________
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> STOP MORE SPAM with the new MSN 8 and get 2 months FREE*
>>>>>>>>>>>>> http://join.msn.com/?page=features/junkmail
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> --
>>>>>>>>>>>> William D. Penny
>>>>>>>>>>>> Wellcome Department of Imaging Neuroscience
>>>>>>>>>>>> University College London
>>>>>>>>>>>> 12 Queen Square
>>>>>>>>>>>> London WC1N 3BG
>>>>>>>>>>>>
>>>>>>>>>>>> Tel: 020 7833 7478
>>>>>>>>>>>> FAX: 020 7813 1420
>>>>>>>>>>>> Email: [log in to unmask]
>>>>>>>>>>>> URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> _________________________________________________________________
>>>>>>>>>>>
>>>>>>>>>>> Add photos to your messages with MSN 8. Get 2 months FREE*.
>>>>>>>>>>> http://join.msn.com/?page=features/featuredemail
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> --
>>>>>>>>>> William D. Penny
>>>>>>>>>> Wellcome Department of Imaging Neuroscience
>>>>>>>>>> University College London
>>>>>>>>>> 12 Queen Square
>>>>>>>>>> London WC1N 3BG
>>>>>>>>>>
>>>>>>>>>> Tel: 020 7833 7478
>>>>>>>>>> FAX: 020 7813 1420
>>>>>>>>>> Email: [log in to unmask]
>>>>>>>>>> URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> _________________________________________________________________
>>>>>>>>> Add photos to your messages with MSN 8. Get 2 months FREE*.
>>>>>>>>> http://join.msn.com/?page=features/featuredemail
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>>> William D. Penny
>>>>>>>> Wellcome Department of Imaging Neuroscience
>>>>>>>> University College London
>>>>>>>> 12 Queen Square
>>>>>>>> London WC1N 3BG
>>>>>>>>
>>>>>>>> Tel: 020 7833 7478
>>>>>>>> FAX: 020 7813 1420
>>>>>>>> Email: [log in to unmask]
>>>>>>>> URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> _________________________________________________________________
>>>>>>> MSN 8 helps eliminate e-mail viruses. Get 2 months FREE*.
>>>>>>> http://join.msn.com/?page=features/virus
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>>
>>>>>> --
>>>>>> William D. Penny
>>>>>> Wellcome Department of Imaging Neuroscience
>>>>>> University College London
>>>>>> 12 Queen Square
>>>>>> London WC1N 3BG
>>>>>>
>>>>>> Tel: 020 7833 7478
>>>>>> FAX: 020 7813 1420
>>>>>> Email: [log in to unmask]
>>>>>> URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
>>>>>>
>>>>>>
>>>>>
>>>>> _________________________________________________________________
>>>>> Tired of spam? Get advanced junk mail protection with MSN 8.
>>>>> http://join.msn.com/?page=features/junkmail
>>>>>
>>>>>
>>>>>
>>>>
>>>>
>>>> --
>>>> William D. Penny
>>>> Wellcome Department of Imaging Neuroscience
>>>> University College London
>>>> 12 Queen Square
>>>> London WC1N 3BG
>>>>
>>>> Tel: 020 7833 7478
>>>> FAX: 020 7813 1420
>>>> Email: [log in to unmask]
>>>> URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
>>>>
>>>>
>>>
>>> _________________________________________________________________
>>> MSN 8 helps eliminate e-mail viruses. Get 2 months FREE*.
>>> http://join.msn.com/?page=features/virus
>>>
>>>
>>>
>>
>>
>> --
>> William D. Penny
>> Wellcome Department of Imaging Neuroscience
>> University College London
>> 12 Queen Square
>> London WC1N 3BG
>>
>> Tel: 020 7833 7478
>> FAX: 020 7813 1420
>> Email: [log in to unmask]
>> URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
>>
>>
>
> _________________________________________________________________
> Add photos to your messages with MSN 8. Get 2 months FREE*.
> http://join.msn.com/?page=features/featuredemail
>
> ------------------------------------------------------------------------
>
> spmfig_03Jun2004_4.jpg
>
> Content-Type:
>
> image/pjpeg
> Content-Encoding:
>
> base64
>
>


--
William D. Penny
Wellcome Department of Imaging Neuroscience
University College London
12 Queen Square
London WC1N 3BG

Tel: 020 7833 7478
FAX: 020 7813 1420
Email: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~wpenny/

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