# Estimation of the shape parameter of gamma distribution in Winbugs

I want to estimate the shape parameter of gamma distribution in Winbugs. I select gamma distribution as prior for shape parameter. Data set is generated using MATLAB as:

gamrnd(5,1,[100 1])


a small part of data loaded to model is here:

list(n=100,b=1)
y[,1]
9.85509822926424
6.78794280129914
2.37341388433267
5.44664020179438
14.7723695566505
4.53177357981821
.
.
END


The model in Winbugs is simple and as follows:

model;
{
for( i in 1 : n ) {
y[i] ~ dgamma(a,b)
}
a ~ dgamma(3,1)
}


Estimation is strongly dependent on the prior that was selected for a. As for each distribution, (normal-gamma-uniform) the estimated a value is around the mean value of the selected prior distribution. For example, choosing the above-mentioned prior (a ~ dgamma(3,1)) resulted in shape parameter estimation 3.026; also running the model for more iterations doesn't change results so much!

What is the problem and how can I solve that?

## 1 Answer

I run a similar script in R, but it seems that OK, setting prior of the b

How is your prior of b setting?

Has your MCMC chain already converged?

PS: I tried something as below as you set b as fixed. But I also tried some other prior of b, it is OK.

N <- 100
x <- rgamma(N, 5, 1)

write("
model {
for (i in 1:length(x)) {
x[i] ~ dgamma(a, b)
}
a ~ dgamma(3, 1)
b <- 1
}",
file="example1.bug")

jags <- jags.model('example1.bug',
data = list('x' = x),
n.chains = 4,
n.adapt = 100)

mcmc.samples <- coda.samples(jags,
c('a', "b"),
n.iter = 10000)

summary(mcmc.samples)

• yes coverage is occurred! i supposed b to be constant and the data set is added to question. – user110502 Nov 26 '13 at 11:53
• may i ask you for the R script for this model? – user110502 Nov 26 '13 at 11:58
• @user110502 it seems that other b's prior like log-normal I tried is also OK. But you could try the script above. – Shusheng Nov 26 '13 at 12:11
• @user110502 Note that asking for code (arguably) takes this off-topic. Your original question floats somewhere between statistics and statistical computing, but the help for CV does spell out that questions focused entirely on code belong elsewhere. – Nick Cox Nov 26 '13 at 12:13