Dear BUGS users.
I have a probably trivial BUGS modelling problem concerning a statistical
inference of life times data.
I have a series of 44 observed life times, some are actually observed life
times, and oters are left censored.
I would like to model the underlying Survivor as Weibull pdf, with three
parameters: the usual shape and scale
parameters, and a location parameter: S(t|gamma,eta,mu)=exp(-((t-mu)/eta)
**gamma).
My assumptions about each parameter priors are:
* for (mu), uniformlili distributed from 0 to 3.15 (the min observed life
time)
* for gamma (Weibull shape factor) a Gamma(a,b)=Gamma(1.4,1.18)
* for eta , a Gamma(a,b)=Gamma(0.25,20).
My problem is "how can I model the Weibull location parameter"?
What is wrong in a model like this:
model {
mu ~ dunif(0,3.15)
gamma ~ dgamma(1.4,1.18)
eta ~ dgamma(0.25,20)
lambda <- pow(1/pow(eta,gamma))
for (i in 1:N) {
censored_offset[i] <- censored[i] - mu
t[i] ~ dweib(gamma,lambda) I (censored_offset[i], )
}
}
list (N=44, t=c(NA, .., <observed life time>, ...),
censored=c(<censored life time>, 0.0, ....))
What are the differences with:
model {
gamma ~ dgamma(1.4,1.18)
eta ~ dgamma(0.25,20)
lambda <- pow(1/pow(eta,gamma))
for (i in 1:N) {
mu[i]~dunif(0.3,3.15)
censored_offset[i] <- censored[i] - mu[i]
t[i] ~ dweib(gamma,lambda) I (censored_offset[i], )
}
}
and with
model {
mu ~ dunif(0,3.15)
gamma ~ dgamma(1.4,1.18)
eta ~ dgamma(0.25,20)
lambda <- pow(1/pow(eta,gamma))
censored_offset1:N] <- censored[1:N] - mu
for (i in 1:N) {
t[i] ~ dweib(gamma,lambda) I (censored_offset[i], )
}
}
More in general, what are the advices to properly manage location
parameters in presence of censored data?
Thanks for your support
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