BUGS/JAGS Fundamentals

When to Use This Skill

• Writing new WinBUGS or JAGS models
• Understanding BUGS declarative syntax
• Converting between BUGS and Stan
• Integrating with R via R2jags or R2WinBUGS

Model Structure

BUGS uses a single declarative block where order doesn't matter:

model {
  # Likelihood (order doesn't matter)
  for (i in 1:N) {
    y[i] ~ dnorm(mu[i], tau)
    mu[i] <- alpha + beta * x[i]
  }

  # Priors
  alpha ~ dnorm(0, 0.001)
  beta ~ dnorm(0, 0.001)
  tau ~ dgamma(0.001, 0.001)

  # Derived quantities
  sigma <- 1 / sqrt(tau)
}

CRITICAL: Precision Parameterization

BUGS uses PRECISION (tau = 1/variance), NOT standard deviation:

dnorm(mu, tau)

dmnorm(mu[], Omega[,])

Converting SD ↔ Precision

# Precision from SD
tau <- pow(sigma, -2)

# SD from precision
sigma <- 1 / sqrt(tau)

Distribution Reference

Continuous (All use precision!)

y ~ dnorm(mu, tau)        # Normal: tau = 1/sigma²
y ~ dlnorm(mu, tau)       # Log-normal (log-scale)
y ~ dt(mu, tau, df)       # Student-t
y ~ dunif(lower, upper)   # Uniform
y ~ dgamma(shape, rate)   # Gamma
y ~ dbeta(a, b)           # Beta
y ~ dexp(lambda)          # Exponential (rate)
y ~ dweib(shape, lambda)  # Weibull
y ~ ddexp(mu, tau)        # Double exponential

Discrete

y ~ dbern(p)              # Bernoulli
y ~ dbin(p, n)            # Binomial (p first!)
y ~ dpois(lambda)         # Poisson
y ~ dnegbin(p, r)         # Negative binomial
y ~ dcat(p[])             # Categorical
y ~ dmulti(p[], n)        # Multinomial

Multivariate

y[1:K] ~ dmnorm(mu[], Omega[,])    # MVN (precision matrix!)
Omega[1:K,1:K] ~ dwish(R[,], df)   # Wishart (for precision)
p[1:K] ~ ddirch(alpha[])           # Dirichlet

Syntax Essentials

Stochastic vs Deterministic

# Stochastic (random variable)
y ~ dnorm(mu, tau)

# Deterministic (function)
mu <- alpha + beta * x

Loops

for (i in 1:N) {
  y[i] ~ dnorm(mu[i], tau)
}

Truncation (JAGS)

y ~ dnorm(mu, tau) T(lower, upper)
y ~ dnorm(mu, tau) T(0, )     # Lower only

Logical Functions (JAGS)

ind <- step(y - threshold)   # 1 if y >= threshold
eq <- equals(y, 0)           # 1 if y == 0

Common Priors

# Vague normal (variance = 1000)
alpha ~ dnorm(0, 0.001)

# Half-Cauchy on SD (via uniform)
sigma ~ dunif(0, 100)
tau <- pow(sigma, -2)

# Vague gamma on precision
tau ~ dgamma(0.001, 0.001)

# Correlation matrix
Omega ~ dwish(I[,], K + 1)

R Integration

R2jags (Recommended)

library(R2jags)

jags.data <- list(N = 100, y = y, x = x)
jags.params <- c("alpha", "beta", "sigma")
jags.inits <- function() {
  list(alpha = 0, beta = 0, tau = 1)
}

fit <- jags(
  data = jags.data,
  inits = jags.inits,
  parameters.to.save = jags.params,
  model.file = "model.txt",
  n.chains = 4,
  n.iter = 10000,
  n.burnin = 5000
)

print(fit)
fit$BUGSoutput$summary

R2WinBUGS (Windows)

library(R2WinBUGS)

fit <- bugs(
  data = bugs.data,
  inits = bugs.inits,
  parameters.to.save = bugs.params,
  model.file = "model.txt",
  n.chains = 3,
  n.iter = 10000,
  bugs.directory = "C:/WinBUGS14/"
)

Key Differences from Stan

dnorm(mu, tau)

normal(mu, sigma)

dmnorm(mu, Omega)

multi_normal(mu, Sigma)

Common Errors

1. Using SD instead of precision:

   dnorm(0, 1)

   means variance=1, NOT SD=1
2. Wrong binomial order:

   dbin(p, n)

   not

   dbin(n, p)

3. Missing initial values: Provide inits for complex models
4. Invalid parent values: Check for NA/NaN in data