Hello,
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 tests. 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].
cheers, Thomas ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
