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STS563 Davide Di Cecco et al.
3. Simulations
We report the results of a simulation for empirically assessing the
proposed algorithm. We considered 5 lists, A, B, C, D, E, and defined a scenario
with three strata: one with all sources, one where 4 out of five sources operate,
and another one where just three sources operate. We set N = 10000 and a
proportion of out–of–scope units (both captured and non-captured) equal to
40%, so that the desired total N1 is 6000 in expectation. The model parameters
have been set in such a way that the proportion of unobserved units (both in–
scope and out–of–scope) is about 30%.
Model selection is a critical issue for capture–recapture modeling as
population size estimate can be sensitive to changes in the parameterization. To
have a hint on the robustness of the procedure under mis-specification of the
model, we generated a sample from model [XABC][XD][XE], and estimated N1
under two different models: the CIA model [XA][XB][XC][XD][XE], and the (non –
decomposable) model including all 15 second order interactions but no higher
order parameters. Results regarding the second model can be viewed in Figure
1, where one sees that the true value of N1 is comprised in the 95% credibility
interval, despite 5 parameters are missing (those relative to [ABC], [XAB], [XAC],
[XBC] and [XABC]).

FIGURE 1. Posterior distributions of N1 under the generating model [XABC][XD][XE] (left) and
under the all–second–order–interactions model (right). The orange line indicates the true
value of N1, the gray area the 95% HPD.

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