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:
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 63.639We 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.
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.
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/RtmpscETcs/file35a74dfd4429', 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 2024-01-30 09:20:56.215422.
#
# mean sd 2.5% 50% 97.5% overlap0 f Rhat n.eff
# alpha 51.843 0.794 50.251 51.838 53.489 FALSE 1 1.004 381
# beta 0.035 0.002 0.031 0.035 0.039 FALSE 1 1.004 374
# sigma 0.726 0.162 0.483 0.695 1.095 FALSE 1 1.005 623
# deviance 33.534 3.100 30.089 32.588 41.013 FALSE 1 1.009 397
#
# 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 = 38.327
# 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/RtmpscETcs/file35a74dfd4429', 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 2024-01-30 09:20:57.296598.
#
# mean sd 2.5% 50% 97.5% overlap0 f Rhat n.eff
# alpha 51.826 0.714 50.210 51.878 53.102 FALSE 1 1.025 80
# beta 0.035 0.002 0.031 0.035 0.039 FALSE 1 1.020 100
# sigma 0.717 0.144 0.485 0.704 1.025 FALSE 1 1.002 450
# mu[1] 59.982 0.334 59.339 59.998 60.534 FALSE 1 1.029 72
# mu[2] 60.857 0.298 60.265 60.871 61.358 FALSE 1 1.028 73
# mu[3] 60.809 0.300 60.215 60.823 61.312 FALSE 1 1.028 73
# mu[4] 61.733 0.264 61.192 61.752 62.216 FALSE 1 1.028 74
# mu[5] 63.278 0.215 62.801 63.290 63.662 FALSE 1 1.024 85
# mu[6] 63.906 0.200 63.459 63.912 64.264 FALSE 1 1.022 95
# mu[7] 64.546 0.189 64.107 64.553 64.893 FALSE 1 1.018 115
# mu[8] 64.467 0.191 64.032 64.472 64.816 FALSE 1 1.018 112
# mu[9] 65.663 0.183 65.263 65.666 66.017 FALSE 1 1.010 196
# mu[10] 66.419 0.189 66.003 66.422 66.768 FALSE 1 1.005 320
# mu[11] 67.240 0.203 66.814 67.248 67.618 FALSE 1 1.002 450
# mu[12] 67.302 0.204 66.873 67.310 67.682 FALSE 1 1.002 450
# mu[13] 68.630 0.241 68.119 68.640 69.106 FALSE 1 1.001 450
# mu[14] 69.323 0.265 68.747 69.332 69.879 FALSE 1 1.002 450
# mu[15] 69.865 0.286 69.260 69.875 70.457 FALSE 1 1.003 395
# mu[16] 71.143 0.338 70.451 71.142 71.843 FALSE 1 1.005 288
# deviance 33.176 2.593 30.003 32.583 39.958 FALSE 1 1.009 231
#
# 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 = 3.3 and DIC = 36.524
# 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')