Abstract：
:Link et al. (2010, Biometrics 66, 178-185) define a general framework for analyzing capture-recapture data with potential misidentifications. In this framework, the observed vector of counts, y, is considered as a linear function of a vector of latent counts, x, such that y=Ax, with x assumed to follow a multinomial distribution conditional on the model parameters, θ. Bayesian methods are then applied by sampling from the joint posterior distribution of both x and θ. In particular, Link et al. (2010) propose a Metropolis-Hastings algorithm to sample from the full conditional distribution of x, where new proposals are generated by sequentially adding elements from a basis of the null space (kernel) of A. We consider this algorithm and show that using elements from a simple basis for the kernel of A may not produce an irreducible Markov chain. Instead, we require a Markov basis, as defined by Diaconis and Sturmfels (1998, The Annals of Statistics 26, 363-397). We illustrate the importance of Markov bases with three capture-recapture examples. We prove that a specific lattice basis is a Markov basis for a class of models including the original model considered by Link et al. (2010) and confirm that the specific basis used in their example with two sampling occasions is a Markov basis. The constructive nature of our proof provides an immediate method to obtain a Markov basis for any model in this class.
journal_name
Biometricsjournal_title
Biometricsauthors
Schofield MR,Bonner SJdoi
10.1111/biom.12333subject
Has Abstractpub_date
2015-12-01 00:00:00pages
1070-80issue
4eissn
0006-341Xissn
1541-0420journal_volume
71pub_type
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