Ecological Archives E088-117-A5

Chaozhi Zheng, Otso Ovaskainen, Marjo Saastamoinen, and Ilkka Hanski. 2007. Age-dependent survival analyzed with Bayesian models of mark–recapture data. Ecology 88:1970–1976.

Appendix E. Bayesian regressions of individual deviations against traits.

The full posterior distribution of the model given by Eq. (3) is given by

,

where  with  is  identity matrix and  is the dimension of vector , and  is the marginal posterior distribution of the individual deviations in capture probabilities, which is obtained from the main model, and used here as a prior distribution. For the parameters , , and  we used a non-informative prior distribution . The full conditional posterior distributions used in the Gibbs sampling are given as follows.

1. The full conditional posterior distribution of  is given by

.

The ’s were sampled using the Metropolis-Hastings algorithm with proposal distribution .

2. The full conditional posterior distribution of the parameters , , and  is given by

.

These parameters were sampled using a standard procedure (Gelman et al. 2004), which involves two steps. (i)  is sampled from the marginal posterior distribution , and (ii) and are sampled from the full conditional posterior distribution. Here , , and  are given by

.

LITERATURE CITED

Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin. 2004. Bayesian data analysis. Chapman and Hall/CRC.



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