Proceedings of the First Symposium on Marsupials in New Zealand
Appendix — Statistical basis for the model
Appendix
Statistical basis for the model
From the first premise that the density and hence probability of encounter remains constant from night to night, and animals are simply remembering bait station locations, we have:
P1(0) = P2(0) ----------------------= Pt(0)
where Pt(0) is the probability of non-encounter at time t.
Now n1/N = n2/n1-----------------------------------= nt/nt-1
where nt is the no. of baits remaining at night t, and N is the total bait stations set.
page 194Thus the probability of non-encounter up to and including night t is and the probability of n encounters during the t nights can be shown to be
This is a Poisson process, obtained from the superimposition of several independent Poisson processes (Bailey 1964, Cox and Miller 1965). The distribution function can be regarded as a composite one of a Poisson density function and an exponential time function (Bailey 1964) representing the time between encounters.
Thus an estimate of density dt can be obtained from (1):