Dear Peter, Glad et al,
This is great advice from Glad below.
It's probably worth adding that Bayesian inference at the 2nd level is considerably quicker (eg just a few minutes, possibly tens of minutes)
The main reason for this is that there are usually many fewer images than at the first level - tens rather than hundreds.
The procedure here is to Specify a 2nd level model - t-tests, ANOVA etc - then estimate it with the Classical option
(you can also play with some contrasts here). Then estimate the model again using the Bayesian 2nd level option and you can create parameter inference and model comparison maps  by specifying contrasts in the usual way.
Its perfectly valid to compare parameters to a threshold of zero.
Importantly, the data going into this analysis can be any set of con*.images from a first level analysis - ie from the usual classical SPM first level model. You don't have to also do Bayesian analysis at the first level.
If you're going to HBM this year, you might like to come to the education session on the Sunday - I'll be giving a talk on PPMs.
All the best,
 W. Penny and G. Ridgway (2013). Efficient Posterior Probability Mapping using Savage-Dickey Ratios. PLoS One 8(3), e59655
> -----Original Message-----
> From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]]
> On Behalf Of Paul Glad Mihai
> Sent: 29 May 2014 09:42
> To: [log in to unmask]
> Subject: Re: [SPM] Second level bayesian modelling - Activation threshold =
> Dear Peter,
> Bayesian inference has some advantages over the frequentist approach (also
> termed classical for some reason, but classical statistics is even older than
> frequentist statistics... that's another topic):
> * you don't have to correct for multiple comparisons, although some might
> disagree (see Woolrich 2012, Neuroimage)
> * your answer will be a probability that the effect is there given the data, as
> opposed to rejecting the null hypothesis given a small enough p-value
> * with frequentist inference having a lot of data or sensitivity can declare an
> activation for every voxel in the brain, i.e. it will reject the null hypothesis for
> for every voxel in the brain
> * in SPM for first level Bayesian inference a spatial regularization prior is used
> on the unsmoothed data, meaning that the smoothing is automatic -- a much
> better approach than smoothing with a fixed width kernel over the whole
> * you can compare non-nested models, something you can't do with
> frequentist inference (Rosa, 2010 Neuroimage; Harrison, 2011; Frontiers in
> Human Neuroscience)
> If you look at the examples in the SPM manual will get a bit of an idea of the
> steps you need to take in Bayesian inference in SPM. However it doesn't tell
> you much about 2nd level inference. Regardless, I would suggest you go
> through those examples step by step. What you will find, and what I found
> was that Bayesian inference finds expected activations where the
> frequentist approach doesn't -- so you could say it is more specific, although
> that's not really a right term to use in Bayesian statistics.
> The biggest drawback is the long computation time. Just to give you an idea,
> on an 8 core intel i5 with 8 parallelized processes it took around
> 26 hours for 51 subjects with one session each for the first level Bayesian
> estimation. Mind you I also asked for the log model evidence.
> To get an idea of Bayesian inference I would first suggest you look at the
> videos on the SPM website, specifically:
> I would watch both!
> Concerning reading material you can take a look at the SPM book chapters
> 22,23 maybe 24 and maybe 25. The latter two are maths heavy. You can find
> some of the PDFs on the SPM website
> If you need a general overview of Bayesian statistics then check out
> Kruschke's Doing Bayesian Data Analysis or his video on it:
> And if you really want to get into Bayesian statistics then check out David
> Draper's video lectures and exercises:
> And last but not least, the scholaropedia entry for Bayesian statistics is nice
> and short:
> I hope this helps!
> Have fun with Bayes!
> On 29.05.2014 01:02, SPM automatic digest system wrote:
> > Date: Tue, 27 May 2014 23:34:09 +0000
> > From: Peter Goodin <[log in to unmask]>
> > Subject: Second level bayesian modelling - Activation threshold = 0?
> > Hi SPM list,
> > I'm doing a second level analysis on my fmri data and have been reading
> about the Bayesian method, which for my interests has been suggested to
> be robust to the effects of outliers (is this true)?
> > Having a read through the mailing list I see that the initial PPM threshold
> doesn't have to be used but I was wondering if it's acceptable to have y = 0?
> > Can anyone recommend some further reading on the pros and cons of low
> threshold PPMs?
> > Thanks,
> > Peter
> Glad MIHAI, M.Sc. Biomedical Physics
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