# JAGS Tutorial

JAGS is a language that allows you to run Bayesian analyses. It gets at the posterior by generating samples based on the posterior and statistical model.

You’ll need to download and install JAGS. You can interact with JAGS through one of three R packages:

• runjags (recommended for this course)
• Model written as a single string in R; possibly also allows you to input from file.
• Quick-start guide vignette: vignette("quickjags", package="runjags")
• Full user guide vignette: vignette("UserGuide", package="runjags")
• rjags (sample code here)
• Model read in from plain text file.
• R2jags
• this is dependent on R2winbugs, which I find doesn’t work well outside of Windows machines, so I’m more hesitant to use this package.
• Model written in R as a function, but using JAGS language; or inputted from file.

Also, the coda package is useful for working with the output of at least runjags.

• Generates samples of parameters based on the prior and statistical model.
• Need to specify which parameters you want to include in the output (aka “track” or “monitor”).
• Specify probability distributions similarly to R, except:
• Draw samples using calls like dexp and dnorm, not rexp and rnorm.
• The JAGS version of rnorm uses the precision (=1/variance) instead of standard deviation. The documentation of JAGS code is not as nice as R. You have to look things up from a table-of-contents-style search from this document. Page 29 shows the aliases for various distributions.

For this week’s lab assignment (3), you’ll only be using it to generate observations from a distribution. Let’s generate data from a N(0,2) distribution (that is, variance=2), and ignore the warning messages for this week.

suppressPackageStartupMessages(library(runjags))
my_model <- "
model{
# This is a comment.
theta ~ dnorm(0, 1/2)
}
"
fit <- run.jags(my_model, monitor="theta", n.chains=1, sample=1000)
## Warning: No data was specified or found in the model file so the simulation was
## run withut data
## Calling the simulation...
## Welcome to JAGS 4.3.0 on Tue Sep 22 22:14:03 2020
## JAGS is free software and comes with ABSOLUTELY NO WARRANTY
## . . Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 0
##    Unobserved stochastic nodes: 1
##    Total graph size: 5
## . Initializing model
## . Updating 4000
## -------------------------------------------------| 4000
## ************************************************** 100%
## . . Updating 1000
## -------------------------------------------------| 1000
## ************************************************** 100%
## . . . . Updating 0
## . Deleting model
## .
## Note: the model did not require adaptation
## Simulation complete.  Reading coda files...
## Calculating summary statistics...
## Warning: Convergence cannot be assessed with only 1 chain
## Finished running the simulation
theta <- coda::as.mcmc(fit)
head(theta)
## Markov Chain Monte Carlo (MCMC) output:
## Start = 5001
## End = 5007
## Thinning interval = 1
##          theta
## 5001  0.412988
## 5002 -1.439260
## 5003  0.520555
## 5004  1.702830
## 5005  0.840491
## 5006  1.610820
## 5007  1.567480
plot(theta)

## More sample code

library(tidyverse)
## ── Attaching packages ───────────────────────────────────────────────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.2     ✓ purrr   0.3.4
## ✓ tibble  3.0.3     ✓ dplyr   1.0.2
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.3.1     ✓ forcats 0.5.0
## ── Conflicts ──────────────────────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::lag()     masks stats::lag()
library(runjags)
n <- 50
dat <- tibble(x=rnorm(n),
y=x + rnorm(n))
jagsdat <- c(as.list(dat), n=nrow(dat))
model <- "model{
for (i in 1:n) {
y[i] ~ dnorm(beta*x[i], tau)
}
tau <- pow(sigma, -2)
sigma ~ dunif(0, 100)
beta ~ dnorm(0, 0.001)
}"
foo <- run.jags(
model=model,
monitor=c("beta0", "beta1", "sigma"),
data=jagsdat
)
## Warning: No initial value blocks found and n.chains not specified: 2 chains were
## used
## Warning: No initial values were provided - JAGS will use the same initial values
## for all chains
## Calling the simulation...
## Welcome to JAGS 4.3.0 on Tue Sep 22 22:14:07 2020
## JAGS is free software and comes with ABSOLUTELY NO WARRANTY
## . . Reading data file data.txt
## . Compiling model graph
##    Resolving undeclared variables
##    Allocating nodes
## Graph information:
##    Observed stochastic nodes: 50
##    Unobserved stochastic nodes: 2
##    Total graph size: 159
## . Initializing model
## -------------------------------------------------| 1000
## ++++++++++++++++++++++++++++++++++++++++++++++++++ 100%
## . Updating 4000
## -------------------------------------------------| 4000
## ************************************************** 100%
## . Failed to set trace monitor for beta0
## . Failed to set trace monitor for beta1
## . . Updating 10000
## -------------------------------------------------| 10000
## ************************************************** 100%
## . . . . . Updating 0
## . Deleting model
## .
## Simulation complete.  Reading coda files...
## Finished running the simulation
plot(coda::as.mcmc(foo))
## Warning in as.mcmc.runjags(foo): Combining the 2 mcmc chains together