bugs-fundamentals

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:

Distribution	BUGS Syntax	Meaning
Normal	dnorm(mu, tau)	tau = 1/sigma²
MVN	dmnorm(mu[], Omega[,])	Omega = inverse(Sigma)

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