* Shape = 2, scale = 4.5 (relatively uninformative)
* Shape = 4.5, scale = 2 (relatively informative)
I conducted the analysis under two model settings:
* By ensuring independence between sites. This resulted in R values of 32, 15, 13 and 8 for
home range sizes 10 km2, 18 km2, 25 km2 and 50 km2 respectively. An example of such an
arrangement is shown in Figure 3-5 for the 10 km2 sites.
* By relaxing the assumption of independence between sites. Here, I assumed that the
average abundance in each cell remains constant. This resulted in R values of 116, 79, 58
and 35 for home range sizes 10 km2, 18 km2, 25 km2 and 50 km2 respectively. An example
of such an arrangement is shown in Figure 3-6 for the 10 km2 sites.
The Gibbs sampler was run 100,000 times and the first 30,000 iterations were left out in
the calculations of the statistics, called the "bum-in period". I checked for auto-correlation and
thinned the results from the remaining 70,000 draws to ensure that independent and identically
distributed (iid) draws are made for the calculations of the statistics. The analysis has been run
on one subjective selection of sites based on assumed home range sizes. This selection is based
on the criterion that two sites are separated by at least one home-range diameter and does
spatially cover the area systematically. Hence, I did not consider it worthy of an effort to derive
estimates of the two parameters with other similar selections with the expectation of similar
results.
Results
Assuming independence between sites. The posterior summary statistics for the results
by ensuring independence between sites are tabulated (Tables 3-3 and 3-4). For the two prior
distributions (Figures 3-7 and 3-8) considered, gamma(2, 4.5) has a mean of 9 and a standard
deviation of 6.364 while gamma(4.5, 2) has a mean of 9 and a standard deviation of 4.243.
The mean estimates of animal-specific detection probabilities are considerably low
(between 0.0377 to 0.1055). The posterior standard deviations for the estimates of either r or 2 in
an analysis for a given year did not vary by much. There is a reduction in the variability of the