Cecile and Joe,
Thank you for the replies. That helped clear up a lot for me.
And thank you for the link Cecile. Estimating sigma_phy is quite a pain
because of all the matrix inversions. I've a tree of approx. 2000 tips, so
even using of a Cholesky decomposed V_{phy} doesn't buy me much time at all.
Because the vector of means for the MVN in my work is all 0s, I've written
my own MVN sampler to try and minimize how many inversions or determinants
need to be calculated. The stan mailing list had a great little discussion
on how to speed up estimation of MVN random effects with partially known
covariance matrices
https://groups.google.com/forum/#!topic/stan-users/HcvYaDu71_Y and I just
followed that code. Now my posterior sampling at least gets off the ground
and finishes.
The stan list discussion possibly provides a useful starting template for
other people on this list trying to do similar things.
Cheers,
Peter
On Mon, Dec 22, 2014 at 11:32 AM, Cecile Ane <a...@stat.wisc.edu> wrote:
> Hi Peter,
>
> We have taken a similar approach in this paper:
> http://onlinelibrary.wiley.com/doi/10.1111/evo.12582/abstract
> We also use a Bayesian approach, with a prior that allows us to integrate
> the ancestral state and the total variance analytically (no need for MCMC
> for those parameters). Our notation for your sigma_phy is lambda, like
> Pagel's, and we do use multiple individuals per species. For what it's
> worth.
>
> Regarding the scaling of branch lengths, I agree with Joe that there is
> nothing particular about 1, other than providing an easier interpretation
> for the numerical value of the phylogenetic variance.
> Cheers,
> Cecile.
>
>
> On 12/14/2014 01:03 PM, Peter Smits wrote:
>
>> Hi list,
>>
>> I have a similar question to Edwin. I too am working with a hierarchical
>> Bayesian model, though I've implemented it in stan. I've included a
>> phylogenetic random effect term, which is modeled as being distributed as
>> multivariate normal with known covariance matrix up to a constant,
>> sigma_{phy}. This follows Lynch '91 Am Nat and Housworth et al. '04 Am Nat
>> by drawing on the similarity with the "animal model" from quantitative
>> genetics.
>>
>> My question is about the scaling of the covariance matrix: is it necessary
>> to have the the diagonal terms satisfy x <= 1 and all the off diagonals to
>> be 0 <= x < 1? I have a time scaled phylogeny from which I have my
>> covariance matrix, so currently all elements of the matrix are not scaled
>> so that the greatest distance from the root to a tip is 1. Currently, the
>> elements of the matrix are just the sum of the shared branch lengths. Is
>> this appropriate? Why or why not?
>>
>> Any input would be much appreciated.
>>
>> Cheers,
>>
>> Peter Smits
>>
>
>
> --
> Cecile Ane
> Departments of Statistics and of Botany
> University of Wisconsin - Madison
> www.stat.wisc.edu/~ane/
>
> CALS statistical consulting lab:
> www.cals.wisc.edu/calslab/stat_consulting.php
>
>
> _______________________________________________
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>
--
Peter D Smits
Grad student
Committee on Evolutionary Biology
University of Chicago
psm...@uchicago.edu
http://home.uchicago.edu/~psmits/home.html
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