Statistics – Applications
Scientific paper
2010-09-17
Statistics
Applications
Scientific paper
A feature of multinomial models with unknown index $N$ is that the dimension of the parameter space potentially depends on $N$, a complication when fitting models by Markov chain Monte Carlo (MCMC). Two commonly used approaches to this problem are: (i) trans-dimensional reversible jump MCMC and (ii) superpopulation data augmentation. A distinguishing feature of the two approaches is that $N$, and combinatorial terms involving $N$, are not explicit in the superpopulation likelihood. To resolve ambiguity about the relationship between the two approaches we compare them analytically. We show that superpopulation data augmentation is equivalent to trans-dimensional sampling but with a restricted prior on $N$. We highlight potential drawbacks that result from not making $N$ explicit in the likelihood in the superpopulation approach. One advantage of the superpopulation approach has been the availability of easy to use BUGS code. We provide simple BUGS code that implements trans-dimensional reversible jump MCMC for the mark-recapture model $M_h$ that can be readily extended to related models.
Barker Richard J.
Schofield Matthew R.
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