Hi all,

I am not sure whether Jarrod's suggestion is correct but I will echo Ben's
concern regarding Bayes factors calculated from the harmonic mean (nicely
summarized in this blog post by Radford Neal
http://radfordneal.wordpress.com/2008/08/17/the-harmonic-mean-of-the-likelihood-worst-monte-carlo-method-ever/
)

A number of alternatives exist for estimating the marginal likelihood but I
am not sure which ones have been implemented in R at this point.

In phylogenetics, people have found Thermodynamic
Integration<http://sysbio.oxfordjournals.org/content/55/2/195.short>and
Stepping-Stone
Sampling <http://sysbio.oxfordjournals.org/content/60/2/150.short> to be
much better alternatives to the use of the HM but I do not know of
publically available R packages which have implemented them (though
presumably it would not be too difficult a task if one were interested in
doing so)

hope that helps.
matt

On Tue, Aug 28, 2012 at 3:51 AM, Jarrod Hadfield <j.hadfield@ed.ac.uk>wrote:

> Hi,
>
> The fact that the deviance is not calculated after marginalising the
> random effects may also be an issue for Bayes factors, as it can be with
> DIC. But not sure.
>
> Cheers,
>
> Jarrod
>
>
>
> Quoting Ben Bolker <bbolker@gmail.com> on Tue, 28 Aug 2012 02:43:23 +0000
> (UTC):
>
>  Mikhail Matz <matz@...> writes:
>>
>>   Hello - is it possible to calculate hayes factors for MCMCglmm
>>> objects, to compare alternative models?  Mikhail
>>>
>>
>>
>> Well, MCMCglmm gives you a posterior sample for the deviance, so
>> in principle you could calculate the harmonic mean of the likelihood,
>> e.g.
>>
>> data(PlodiaPO)
>> model1<-MCMCglmm(PO~1, random=~FSfamily, data=PlodiaPO, verbose=FALSE)
>>
>> likchain <- exp(-model1$Deviance/2)
>> 1/mean(1/likchain)
>>
>>   these are ridiculously big numbers -- that may have something
>> to do with the way the deviance is scaled.
>>
>>   However, harmonic means are known to be really, really
>> dodgy estimates of the Bayes factor -- see e.g.
>>
>> http://scholarworks.umass.edu/**cgi/viewcontent.cgi<http://scholarworks.umass.edu/cgi/viewcontent.cgi>
>> ?
>>    article=1107&context=astro_**faculty_pubs
>> (warning, broken URL)
>>
>>   Perhaps someone else will contribute something more useful.
>>   You could also use DIC to compare models, although it has
>> its own issues ...
>>
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>>
>>
>>
>
>
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