Biomedical Engineering Reference
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other initial size for S(0) and did not notice signicant dierences of results
between them.
5.2. The Prior Distributions of p
S
(t) and (u)
For the prior distributions, because we have very little information about
the Swiss populations, we will assume uniform prior for and will follow
Box and Tiao
1
to assume P (
2
)/(
2
)
1
. For assessing eects of dierent
prior distributions and because we believe that behaviors of homosexual
populations in the western countries are quite similar, we will also assume
natural conjugate priors with hyper-parameters being estimated using esti-
mates from by Tan and Xiang
13;14
for HIV infection and incubation in the
San Francisco homosexual population.
Given the above prior distributions and givenfS(0); I(0; 0) = I(0)g, by
using procedures given in Section 3, we have derived simultaneously the es-
timates of the HIV infection distribution, the HIV incubation distribution,
the death rates, the immigration rate as well as the number of AIDS cases
over the time span in the Swiss homosexual and bisexual population. The
estimates of the HIV infection, HIV incubation distributions and the num-
bers of the predicted AIDS cases are plotted in Figures 1-3. Given below
we summarize our basic ndings:
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