Installing JAGS
In addition to installing the jagsUI package, we also need to separately install the free JAGS software, which you can download here.
Once that’s installed, load the jagsUI library:
library(jagsUI)
Typical jagsUI Workflow
- Organize data into a named
list - Write model file in the BUGS language
- Specify initial MCMC values (optional)
- Specify which parameters to save posteriors for
- Specify MCMC settings
- Run JAGS
- Examine output
1. Organize data
We’ll use the longley dataset to conduct a simple linear regression.
The dataset is built into R.
data(longley)
head(longley)
# GNP.deflator GNP Unemployed Armed.Forces Population Year Employed
# 1947 83.0 234.289 235.6 159.0 107.608 1947 60.323
# 1948 88.5 259.426 232.5 145.6 108.632 1948 61.122
# 1949 88.2 258.054 368.2 161.6 109.773 1949 60.171
# 1950 89.5 284.599 335.1 165.0 110.929 1950 61.187
# 1951 96.2 328.975 209.9 309.9 112.075 1951 63.221
# 1952 98.1 346.999 193.2 359.4 113.270 1952 63.639
We will model the number of people employed (Employed) as a function of Gross National Product (GNP).
Each column of data is saved into a separate element of our data list.
Finally, we add a list element for the number of data points n.
In general, elements in the data list must be numeric, and structured as arrays, matrices, or scalars.
jags_data <- list(
gnp = longley$GNP,
employed = longley$Employed,
n = nrow(longley)
)
2. Write BUGS model file
Next we’ll describe our model in the BUGS language. See the JAGS manual for detailed information on writing models for JAGS. Note that data you reference in the BUGS model must exactly match the names of the list we just created. There are various ways to save the model file, we’ll save it as a temporary file.
# Create a temporary file
modfile <- tempfile()
#Write model to file
writeLines("
model{
# Likelihood
for (i in 1:n){
# Model data
employed[i] ~ dnorm(mu[i], tau)
# Calculate linear predictor
mu[i] <- alpha + beta*gnp[i]
}
# Priors
alpha ~ dnorm(0, 0.00001)
beta ~ dnorm(0, 0.00001)
sigma ~ dunif(0,1000)
tau <- pow(sigma,-2)
}
", con=modfile)
3. Initial values
Initial values can be specified as a list of lists, with one list element per MCMC chain.
Each list element should itself be a named list corresponding to the values we want each parameter initialized at.
We don’t necessarily need to explicitly initialize every parameter.
We can also just set inits = NULL to allow JAGS to do the initialization automatically, but this will not work for some complex models.
We can also provide a function which generates a list of initial values, which jagsUI will execute for each MCMC chain.
This is what we’ll do below.
inits <- function(){
list(alpha=rnorm(1,0,1),
beta=rnorm(1,0,1),
sigma=runif(1,0,3)
)
}
4. Parameters to monitor
Next, we choose which parameters from the model file we want to save posterior distributions for.
We’ll save the parameters for the intercept (alpha), slope (beta), and residual standard deviation (sigma).
params <- c('alpha','beta','sigma')
5. MCMC settings
We’ll run 3 MCMC chains (n.chains = 3).
JAGS will start each chain by running adaptive iterations, which are used to tune and optimize MCMC performance.
We will manually specify the number of adaptive iterations (n.adapt = 100).
You can also try n.adapt = NULL, which will keep running adaptation iterations until JAGS reports adaptation is sufficient.
In general you do not want to skip adaptation.
Next we need to specify how many regular iterations to run in each chain in total.
We’ll set this to 1000 (n.iter = 1000).
We’ll specify the number of burn-in iterations at 500 (n.burnin = 500).
Burn-in iterations are discarded, so here we’ll end up with 500 iterations per chain (1000 total - 500 burn-in).
We can also set the thinning rate: with n.thin = 2 we’ll keep only every 2nd iteration.
Thus in total we will have 250 iterations saved per chain ((1000 - 500) / 2).
The optimal MCMC settings will depend on your specific dataset and model.
6. Run JAGS
We’re finally ready to run JAGS, via the jags function.
We provide our data to the data argument, initial values function to inits, our vector of saved parameters to parameters.to.save, and our model file path to model.file.
After that we specify the MCMC settings described above.
out <- jags(data = jags_data,
inits = inits,
parameters.to.save = params,
model.file = modfile,
n.chains = 3,
n.adapt = 100,
n.iter = 1000,
n.burnin = 500,
n.thin = 2)
#
# Processing function input.......
#
# Done.
#
# Compiling model graph
# Resolving undeclared variables
# Allocating nodes
# Graph information:
# Observed stochastic nodes: 16
# Unobserved stochastic nodes: 3
# Total graph size: 74
#
# Initializing model
#
# Adaptive phase, 100 iterations x 3 chains
# If no progress bar appears JAGS has decided not to adapt
#
#
# Burn-in phase, 500 iterations x 3 chains
#
#
# Sampling from joint posterior, 500 iterations x 3 chains
#
#
# Calculating statistics.......
#
# Done.
We should see information and progress bars in the console.
If we have a long-running model and a powerful computer, we can tell jagsUI to run each chain on a separate core in parallel by setting argument parallel = TRUE:
out <- jags(data = jags_data,
inits = inits,
parameters.to.save = params,
model.file = modfile,
n.chains = 3,
n.adapt = 100,
n.iter = 1000,
n.burnin = 500,
n.thin = 2,
parallel = TRUE)
While this is usually faster, we won’t be able to see progress bars when JAGS runs in parallel.
7. Examine output
Our first step is to look at the output object out:
out
# JAGS output for model '/tmp/RtmpX27jnY/file585c369da170', generated by jagsUI.
# Estimates based on 3 chains of 1000 iterations,
# adaptation = 100 iterations (sufficient),
# burn-in = 500 iterations and thin rate = 2,
# yielding 750 total samples from the joint posterior.
# MCMC ran for 0.001 minutes at time 2026-01-08 12:33:41.915696.
#
# mean sd 2.5% 50% 97.5% overlap0 f Rhat n.eff
# alpha 51.823 0.798 50.208 51.800 53.327 FALSE 1 1.000 750
# beta 0.035 0.002 0.031 0.035 0.039 FALSE 1 1.001 750
# sigma 0.727 0.165 0.493 0.694 1.109 FALSE 1 0.999 750
# deviance 33.496 3.112 30.045 32.747 40.964 FALSE 1 1.006 750
#
# Successful convergence based on Rhat values (all < 1.1).
# Rhat is the potential scale reduction factor (at convergence, Rhat=1).
# For each parameter, n.eff is a crude measure of effective sample size.
#
# overlap0 checks if 0 falls in the parameter's 95% credible interval.
# f is the proportion of the posterior with the same sign as the mean;
# i.e., our confidence that the parameter is positive or negative.
#
# DIC info: (pD = var(deviance)/2)
# pD = 4.8 and DIC = 38.345
# DIC is an estimate of expected predictive error (lower is better).
We first get some information about the MCMC run.
Next we see a table of summary statistics for each saved parameter, including the mean, median, and 95% credible intervals.
The overlap0 column indicates if the 95% credible interval overlaps 0, and the f column is the proportion of posterior samples with the same sign as the mean.
The out object is a list with many components:
names(out)
# [1] "sims.list" "mean" "sd" "q2.5" "q25"
# [6] "q50" "q75" "q97.5" "overlap0" "f"
# [11] "Rhat" "n.eff" "pD" "DIC" "summary"
# [16] "samples" "modfile" "model" "parameters" "mcmc.info"
# [21] "run.date" "parallel" "bugs.format" "calc.DIC"
We’ll describe some of these below.
Diagnostics
We should pay special attention to the Rhat and n.eff columns in the output summary, which are MCMC diagnostics.
The Rhat (Gelman-Rubin diagnostic) values for each parameter should be close to 1 (typically, < 1.1) if the chains have converged for that parameter.
The n.eff value is the effective MCMC sample size and should ideally be close to the number of saved iterations across all chains (here 750, 3 chains * 250 samples per chain).
In this case, both diagnostics look good.
We can also visually assess convergence using the traceplot function:
traceplot(out)
We should see the lines for each chain overlapping and not trending up or down.
Posteriors
We can quickly visualize the posterior distributions of each parameter using the densityplot function:
densityplot(out)
The traceplots and posteriors can be plotted together using plot:
plot(out)
We can also generate a posterior plot manually.
To do this we’ll need to extract the actual posterior samples for a parameter.
These are contained in the sims.list element of out.
post_alpha <- out$sims.list$alpha
hist(post_alpha, xlab="Value", main = "alpha posterior")
Update
If we need more iterations or want to save different parameters, we can use update:
# Now save mu also
params <- c(params, "mu")
out2 <- update(out, n.iter=300, parameters.to.save = params)
# Compiling model graph
# Resolving undeclared variables
# Allocating nodes
# Graph information:
# Observed stochastic nodes: 16
# Unobserved stochastic nodes: 3
# Total graph size: 74
#
# Initializing model
#
# Adaptive phase.....
# Adaptive phase complete
#
# No burn-in specified
#
# Sampling from joint posterior, 300 iterations x 3 chains
#
#
# Calculating statistics.......
#
# Done.
The mu parameter is now in the output:
out2
# JAGS output for model '/tmp/RtmpX27jnY/file585c369da170', generated by jagsUI.
# Estimates based on 3 chains of 1300 iterations,
# adaptation = 100 iterations (sufficient),
# burn-in = 1000 iterations and thin rate = 2,
# yielding 450 total samples from the joint posterior.
# MCMC ran for 0 minutes at time 2026-01-08 12:33:43.025374.
#
# mean sd 2.5% 50% 97.5% overlap0 f Rhat n.eff
# alpha 51.840 0.772 50.356 51.838 53.337 FALSE 1 1.002 450
# beta 0.035 0.002 0.031 0.035 0.039 FALSE 1 1.005 450
# sigma 0.724 0.154 0.490 0.700 1.072 FALSE 1 1.044 126
# mu[1] 59.989 0.360 59.281 59.998 60.702 FALSE 1 0.999 450
# mu[2] 60.863 0.321 60.234 60.879 61.503 FALSE 1 0.999 450
# mu[3] 60.815 0.323 60.182 60.832 61.459 FALSE 1 0.999 450
# mu[4] 61.739 0.283 61.188 61.740 62.289 FALSE 1 0.998 450
# mu[5] 63.282 0.227 62.845 63.275 63.738 FALSE 1 0.999 450
# mu[6] 63.909 0.209 63.511 63.904 64.336 FALSE 1 1.000 450
# mu[7] 64.548 0.196 64.190 64.550 64.939 FALSE 1 1.001 450
# mu[8] 64.469 0.197 64.106 64.470 64.861 FALSE 1 1.001 450
# mu[9] 65.664 0.186 65.307 65.663 66.021 FALSE 1 1.003 450
# mu[10] 66.419 0.190 66.052 66.414 66.773 FALSE 1 1.004 450
# mu[11] 67.240 0.204 66.844 67.228 67.639 FALSE 1 1.005 450
# mu[12] 67.302 0.205 66.901 67.290 67.705 FALSE 1 1.005 450
# mu[13] 68.629 0.244 68.125 68.631 69.144 FALSE 1 1.005 450
# mu[14] 69.321 0.270 68.759 69.327 69.904 FALSE 1 1.006 450
# mu[15] 69.862 0.292 69.255 69.864 70.505 FALSE 1 1.006 450
# mu[16] 71.140 0.348 70.421 71.134 71.921 FALSE 1 1.007 450
# deviance 33.347 2.818 29.962 32.665 40.490 FALSE 1 1.052 95
#
# Successful convergence based on Rhat values (all < 1.1).
# Rhat is the potential scale reduction factor (at convergence, Rhat=1).
# For each parameter, n.eff is a crude measure of effective sample size.
#
# overlap0 checks if 0 falls in the parameter's 95% credible interval.
# f is the proportion of the posterior with the same sign as the mean;
# i.e., our confidence that the parameter is positive or negative.
#
# DIC info: (pD = var(deviance)/2)
# pD = 3.9 and DIC = 37.249
# DIC is an estimate of expected predictive error (lower is better).
This is a good opportunity to show the whiskerplot function, which plots the mean and 95% CI of parameters in the jagsUI output:
whiskerplot(out2, 'mu')
