SOME STATE SPACE MODELS OF AIDS EPIDEMIOLOGY IN HOMOSEXUAL POPULATIONS - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 57

(d) From Figure 2, the estimated density of the HIV incubation distribu-
tion also appeared to be a mixture of distributions with two obvious peaks.
The higher peak occurs at around 320 months after infection and the lower
peak occurs around 232 months after infection in the homosexual popula-
tion. These results seem to suggest a staged model for HIV incubation as
used by many statisticians (see 9, Chapter 4).
(e) From Figure 3, we observe that the estimates of the AIDS incidence
by the Gibbs sampler are almost identical to the corresponding observed
AIDS incidence, suggesting the usefulness of the method. These results
indicate that the estimates by the Gibbs sampler can trace the observed
values very closely if observed values are available.
(f) From results not shown here, it appears that the prior distributions
seem to have little eects on both the HIV infection distribution and the
HIV incubation distribution.
(g) To start the procedure, one needs some initial parameter values for
p S (t) and (u). In this chapter, we rst assumed a Weibull distribution for
the initial incubation distribution with a mean of 10 years and derive es-
timates of the infection distribution by using the standard backcalculation
method 2 . This assumed incubation distribution and the associated estimate
of the infection distribution will then be used to give initial values for the
parameters p S (t) and (u). To check eects of the initial incubation distri-