CHAPTER 2
PARAMETER ESTIMATION OF THE ROYLE AND NICHOLS (2003) MODEL USING
BAYESIAN MARKOV CHAIN MONTE CARLO SIMULATION APPROACH WITH THE
GIBBS SAMPLER ALGORITHM
Introduction
Estimating the number of animals of a particular species in forested areas largely revolves
around addressing two fundamental issues: extrapolation of inferences from a study area and
detection probability (Lancia et al., 1994; Skalski, 1994; Thompson, 1992; Thompson, White &
Gowan, 1998; Yoccoz, Nichols & Boulinier, 2001). First, investigators often have to select
representative areas within a much larger area of interest. However, this fractional area often has
to be estimated and inferences must be extrapolated to the entire area of interest. This is a
standard problem in spatial sampling and statistical texts (Cochran, 1977; Thompson, 1992)
appropriately deal with this issue by permitting such inferences. In field surveys, it is very rare
that investigators detect all animals or signs present even in the fractional area considered.
Instead, data collected reflect some sort of a count statistic that only represents a portion of all
the available detections present. This issue of 'detectability' is the second fundamental issue an
investigator has to deal with in estimating animal abundance. A variety of methods presented in
texts (Buckland et al., 2001; Seber, 1982; Williams et al., 2002) and reviews (Lancia et al.,
1994) provide different methods of estimation of detection probabilities for specific kinds of
count statistics.
Depending on the species studied, the techniques available for gathering appropriate data,
and incorporating the limitations of time, money and effort, often only one or just a few of these
methods are likely to be suitable. For example, capture-recapture methods require repeated
efforts to capture or observe animals (Otis et al., 1978; Pollock et al., 1990). Even observation
based methods such as distance sampling (Buckland et al., 2001) and multiple observers (Cook