# WinBUGS for Population Ecologists: Bayesian Modelling using Markov
chain Monte Carlo (MCMC) Methods

### Gimenez, O., Bonner, S., King, R., Parker, R. A., Brooks, S. P.,
Jamieson, L. E., Grisbois, V., Morgan, B. J. T., Newson, S. and Thomas, L.

## Summary

The computer package WinBUGS is introduced. We first give a brief introduction
to Bayesian theory and its implementation using Markov chain Monte Carlo
(MCMC) algorithms. We then present three case studies showing how WinBUGS
can be used when classical theory is difficult to implement. The first example
uses data on white storks from Baden Wurttemberg, Germany, to demonstrate the
use of mark-recapture models to estimate survival, and also how to cope with
unexplained variance through random effects. Recent advances in methodology
and also the WinBUGS software allow us to introduce (i) a flexible way of
incorporating covariates using spline smoothing and (ii) a method to deal with
missing values in covariates. The second example shows how to estimate
population density while accounting for detectability, using distance sampling
methods applied to a test dataset collected on a known population of wooden
stakes. Finally, the third case study involves the use of state-space models
of wildlife population dynamics to make inferences about density dependence
in a North American duck species. Reversible jump MCMC is used to calculate
the probability of various candidate models. For all example, data and
WinBUGS code are provided.

### Keywords:

Bayesian statistics, density dependence, distance sampling,
external covariates, hierarchical modelling, line transect, mark-recapture,
random effects, reversible jump MCMC, spline smoothing, state-space model,
survival estimation.