[R] MCMC sampling question

Thomas Mang Thomas.Mang at fiwi.at
Wed Aug 12 08:46:32 CEST 2009


Consider MCMC sampling with metropolis / metropolis hastings proposals 
and a density function with a given valid parameter space. How are MCMC 
proposals performed if the parameter could be located at the very 
extreme of the parameter space, or even 'beyond that' ? Example to 
express it and my very nontechnical 'beyond that': The von Mises 
distribution is a circular distribution, describing directional trends. 
It has a concentration parameter Kappa, with Kappa > 0. The lower kappa, 
the flatter the distribution, and for Kappa approaching 0, it converges 
into the uniform. Kappa shall be estimated [in a complex likelihood] 
through MCMC, with the problem that it is possible that there truly 
isn't any directional trend in the data at all, that is Kappa -> 0; the 
latter would even constitute the H0.
If I log-transform Kappa to get in on the real line, will the chain then 
ever fulfill convergence criteria ? The values for logged Kappa should 
be on average I suppose less and less all the time. But suppose it finds 
an almost flat plateau. How do I then test against the H0 - by 
definition, I'll never get a Kappa = 0 exactly; so I can't compare 
against that.

One idea I had: Define not only a parameter Kappa, but also one of an 
indicator function, which acts as switch between a uniform and a 
vonMises distribution. Call that parameter d. I could then for example 
let d switch state with a 50% probability and then make usual acceptance 
Is this approach realistic ? is it sound and solid or nonsense / 
suboptimal? Is there a common solution to the before mentioned problem ?
[I suppose there is. Mixed effects models testing the variances of 
random effects for 0 should fall into the same kind of problem].


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