In JAGS, how can I fix a parameter to a distribution, as opposed to just a constant? The first code chunk below (model1) is a JAGS script designed to estimate a two-group Gaussian mixture model with unequal variances. I am looking for a way to fix one of the parameters (say $\mu_2$) to a particular distribution (e.g., dnorm(0,0.0001)). I know how to fix $\mu_2$ to a constant (e.g., see model2 in code chunk 2), though I cannot find a way to fix $\mu_2$ to my prior belief(e.g., see model3 in code chunk 3, which shows conceptually what I am trying to do).
Thanks in advance!
Code chunk 1
model1 = "
model {

for (i in 1:n1){
y1[i] ~ dnorm (mu1 , phi1) 
}

for (i in 1:n2){ 
y2[i] ~ dnorm (mu2 , phi2) 
}

# Priors
phi1 ~ dgamma(.001,.001) 
phi2 ~ dgamma(.001,.001) 
sigma2.1 <- 1/phi1
sigma2.2 <- 1/phi2
mu1 ~ dnorm (0,0.0001) 
mu2 ~ dnorm (0,0.0001)

# Create a variable for the mean difference

delta <- mu1 - mu2

}
"

Code chunk 2
model2 = "
model {

for (i in 1:n1){
y1[i] ~ dnorm (mu1 , phi1) 
}

for (i in 1:n2){ 
y2[i] ~ dnorm (mu2 , phi2) 
}

# Priors
phi1 ~ dgamma(.001,.001) 
phi2 ~ dgamma(.001,.001) 
sigma2.1 <- 1/phi1
sigma2.2 <- 1/phi2
mu1 ~ dnorm (0,0.0001) 
mu2 <- 1.27

# Create a variable for the mean difference

delta <- mu1 - mu2

}
"

Code chunk 3
model3 = "
model {

for (i in 1:n1){
y1[i] ~ dnorm (mu1 , phi1) 
}

for (i in 1:n2){ 
y2[i] ~ dnorm (mu2 , phi2) 
}

# Priors
phi1 ~ dgamma(.001,.001) 
phi2 ~ dgamma(.001,.001) 
sigma2.1 <- 1/phi1
sigma2.2 <- 1/phi2
mu1 ~ dnorm (0,0.0001) 
mu2 <- dnorm (0,0.0001) 

# Create a variable for the mean difference

delta <- mu1 - mu2

}
"
```


There are at least two ways to express my prior belief of mu2:

*

*I believe very strongly that mu2 can only be a single value, 1.27 say, in which case I can use the assignment operator as shown in chunk2.

*I believe that mu2 is most probably some value, 0 say, but with ~95% probability I think it could be between -0.0002 and 0.0002. In that case I can specify a prior distribution on mu2 as is shown in chunk1.

I think 2. is the answer to the title of the OP.
