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



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

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