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?
They are identical at this point since at least Jags version 4.0.0. See here
The text that is important on that particular post to the jags forum is:
"The Pow function has alias "pow" so it can be invoked either as "a^b" or as "pow(a,b)"
Go ahead and use whichever one you feel more comfortable with. I believe that the use of the original pow function comes from winbugs.