This is probably unimportant, but something I've been curious about for a while.
When constructing a model in JAGS/BUGS, I was initially taught to handle power transformations using the pow() function (e.g. tau <- pow(sigma, -2) to convert from a standard deviation to precision parameter in a normal distribution) but very often, I'll end up using simple arithmetic operators instead.
My question is this: is there a programmatic or syntactic benefit to pow(), or is it just a matter of aesthetics?
By way of an initial exploration, here's a good, long run of a toy simple linear regression, specified both ways. I'm using JAGS, called in R using the R2jags package.
# first some fake data
N <- 1000
x <- 1:N
y <- x + rnorm(N)
# model 1
cat('model {
for (i in 1:N) {
y[i] ~ dnorm(y.hat[i], tau)
y.hat[i] <- a + b * x[i]
}
a ~ dnorm(0, .0001)
b ~ dnorm(0, .0001)
tau <- pow(sigma, -2) ### this is the only difference
sigma ~ dunif(0, 100)
}', file="test1.jags")
# model 2
cat('model {
for (i in 1:N) {
y[i] ~ dnorm(y.hat[i], tau)
y.hat[i] <- a + b * x[i]
}
a ~ dnorm(0, .0001)
b ~ dnorm(0, .0001)
tau <- 1/(sigma*sigma) ### this is the only difference
sigma ~ dunif(0, 100)
}', file="test2.jags")
Both yield essentially equivalent posteriors (not shown, you'll just have to trust me ;) ), and run in essentially equivalent amounts of time.
test.data <- list(x=x,y=y,N=N)
# give both a nice long run
system.time(test1.jags.out <- jags(model.file="test1.jags", data=test.data,
parameters.to.save=c("a","b","tau","sigma"), n.chains=3, n.iter=100000))
user system elapsed
166.85 0.03 166.97
system.time(test2.jags.out <- jags(model.file="test2.jags", data=test.data,
parameters.to.save=c("a","b","tau","sigma"), n.chains=3, n.iter=100000))
user system elapsed
162.42 0.00 162.75
Is there any difference I'm not seeing?
