*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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