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/Rtmpszbrfa/file5ae5b859834', 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 2026-05-29 06:14:19.702614.
#
# mean sd 2.5% 50% 97.5% overlap0 f Rhat n.eff
# alpha 51.823 0.771 50.332 51.807 53.352 FALSE 1 1.000 750
# beta 0.035 0.002 0.031 0.035 0.038 FALSE 1 1.000 750
# sigma 0.722 0.151 0.502 0.696 1.112 FALSE 1 1.014 461
# deviance 33.355 2.917 29.990 32.600 41.608 FALSE 1 1.008 309
#
# 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 = 4.2 and DIC = 37.594
# 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/Rtmpszbrfa/file5ae5b859834', 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 2026-05-29 06:14:20.409269.
#
# mean sd 2.5% 50% 97.5% overlap0 f Rhat n.eff
# alpha 51.904 0.730 50.493 51.885 53.334 FALSE 1 0.999 450
# beta 0.035 0.002 0.031 0.035 0.038 FALSE 1 0.999 450
# sigma 0.724 0.146 0.502 0.697 1.042 FALSE 1 1.003 450
# mu[1] 60.020 0.340 59.365 60.004 60.757 FALSE 1 0.999 450
# mu[2] 60.891 0.303 60.306 60.882 61.583 FALSE 1 0.999 450
# mu[3] 60.843 0.305 60.253 60.833 61.538 FALSE 1 0.999 450
# mu[4] 61.763 0.269 61.270 61.755 62.376 FALSE 1 0.999 450
# mu[5] 63.300 0.217 62.899 63.277 63.795 FALSE 1 0.999 450
# mu[6] 63.924 0.202 63.537 63.904 64.374 FALSE 1 0.998 450
# mu[7] 64.561 0.190 64.206 64.542 64.993 FALSE 1 0.998 450
# mu[8] 64.482 0.191 64.119 64.464 64.918 FALSE 1 0.998 450
# mu[9] 65.673 0.183 65.312 65.665 66.037 FALSE 1 0.998 450
# mu[10] 66.425 0.188 66.067 66.423 66.805 FALSE 1 0.997 450
# mu[11] 67.242 0.202 66.868 67.244 67.647 FALSE 1 0.998 450
# mu[12] 67.303 0.204 66.925 67.307 67.710 FALSE 1 0.998 450
# mu[13] 68.625 0.242 68.175 68.614 69.123 FALSE 1 0.998 450
# mu[14] 69.315 0.266 68.810 69.303 69.869 FALSE 1 0.998 450
# mu[15] 69.854 0.287 69.302 69.840 70.446 FALSE 1 0.998 450
# mu[16] 71.126 0.340 70.481 71.117 71.805 FALSE 1 0.999 450
# deviance 33.203 2.697 30.106 32.500 39.484 FALSE 1 1.000 450
#
# 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 = 3.7 and DIC = 36.853
# 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: