[R-sig-ME] Combining MCMCglmm estimates

[Joshua Wiley]

On Thu, Oct 11, 2012 at 1:05 AM, Hans Ekbrand <hans at sociologi.cjb.net> wrote:
> On Wed, Oct 10, 2012 at 11:56:52AM +0100, Paul Johnson wrote:
>> > Why is different starting values important?
>> > Shouldn't burning make the 10 chains independent enough?
>> ...
>> > The idea that different starting points are needed would, if I
>> > understand the rationale correctly, imply that the chains are
>> > better in the end than in the beginning. Is that the point?
>>
>> I think it's a precaution. Assuming that you have ended up with homogenous looking samples from different runs, you'll be more confident (but never certain of course) that they've converged if they started from different points in parameter space. E.g. there might be local optima where chains could get stuck, and this problem would be much more likely to be discovered starting from different values. I don't know how likely local optima are in practice with a typical MCMCglmm model.
>>
>> However, I don't see that 10 samples of (effective) size 1000 from the same starting values, with sufficient burnin, are any worse than 10,000 samples from a single run. So my feeling is that using different starting values is always worthwhile (given how easy this is), but not strictly essential.
>
> Thanks for your answer, Paul.
>
> 10 different runs with the same starting point would then be just as
> good (or bad) as 1 run, while 10 different runs from different
> starting points would be better. Is that a correct conclusion?

10 different runs would be just as good (or bad) as 1 run, if the
burnin is sufficient. If they are not independent, you gain little.
Using different starting values allows you to make some assessment of
convergence.  Gelman discusses this concept in detail here:
http://stat.columbia.edu/~gelman/research/published/brooksgelman.pdf


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-- 
Joshua Wiley
Ph.D. Student, Health Psychology
Programmer Analyst II, Statistical Consulting Group
University of California, Los Angeles
https://joshuawiley.com/