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:
jagsUI WorkflowlistWe’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 63.639We 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.
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)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.
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).
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.
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.
Our first step is to look at the output object out:
out
# JAGS output for model '/tmp/RtmpyHUD27/file5aea196a69', 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 2026-06-20 10:15:14.180663.
#
# mean sd 2.5% 50% 97.5% overlap0 f Rhat n.eff
# alpha 51.832 0.784 50.336 51.848 53.380 FALSE 1 1.003 633
# beta 0.035 0.002 0.031 0.035 0.039 FALSE 1 1.004 598
# sigma 0.739 0.156 0.510 0.715 1.103 FALSE 1 1.001 750
# deviance 33.474 2.828 30.099 32.814 40.557 FALSE 1 0.999 750
#
# 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 and DIC = 37.48
# 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.
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:
We should see the lines for each chain overlapping and not trending up or down.
We can quickly visualize the posterior distributions of each
parameter using the densityplot function:
The traceplots and posteriors can be plotted together using
plot:
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.
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/RtmpyHUD27/file5aea196a69', 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 2026-06-20 10:15:15.353542.
#
# mean sd 2.5% 50% 97.5% overlap0 f Rhat n.eff
# alpha 51.790 0.757 50.276 51.812 53.266 FALSE 1 1.009 291
# beta 0.035 0.002 0.031 0.035 0.039 FALSE 1 1.010 252
# sigma 0.732 0.168 0.506 0.703 1.129 FALSE 1 1.043 304
# mu[1] 59.960 0.344 59.221 59.975 60.622 FALSE 1 1.006 421
# mu[2] 60.837 0.306 60.179 60.853 61.412 FALSE 1 1.005 450
# mu[3] 60.789 0.308 60.127 60.804 61.369 FALSE 1 1.005 450
# mu[4] 61.715 0.271 61.131 61.733 62.232 FALSE 1 1.003 450
# mu[5] 63.262 0.221 62.812 63.272 63.696 FALSE 1 1.000 450
# mu[6] 63.891 0.207 63.489 63.896 64.287 FALSE 1 0.999 450
# mu[7] 64.532 0.198 64.134 64.535 64.907 FALSE 1 0.999 450
# mu[8] 64.453 0.199 64.056 64.455 64.827 FALSE 1 0.999 450
# mu[9] 65.651 0.198 65.244 65.651 66.042 FALSE 1 1.000 450
# mu[10] 66.408 0.208 65.995 66.417 66.820 FALSE 1 1.001 450
# mu[11] 67.231 0.227 66.779 67.239 67.686 FALSE 1 1.002 436
# mu[12] 67.293 0.229 66.837 67.301 67.748 FALSE 1 1.002 428
# mu[13] 68.623 0.274 68.088 68.627 69.154 FALSE 1 1.004 325
# mu[14] 69.317 0.302 68.740 69.321 69.891 FALSE 1 1.005 299
# mu[15] 69.860 0.325 69.237 69.866 70.464 FALSE 1 1.006 286
# mu[16] 71.141 0.383 70.414 71.143 71.853 FALSE 1 1.007 266
# deviance 33.462 3.301 30.080 32.605 41.456 FALSE 1 1.043 327
#
# 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 = 5.4 and DIC = 38.902
# 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: