From: Bayesian Models for Astrophysical Data, Cambridge Univ. Press

(c) 2017,  Joseph M. Hilbe, Rafael S. de Souza and Emille E. O. Ishida

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# Data from code 5.3

set.seed(1056)                                                                # set seed to replicate example

nobs = 5000                                                                   # number of observations in model

x1 <- runif(nobs)                                                           # random uniform variable

xb <- 2 + 3*x1                                                               # linear predictor, xb

y <- rlnorm(nobs, xb, sdlog=1)                                     # create y as random lognormal variate

Code 5.4 Lognormal model in R using JAGS

==================================================

require(R2jags)

X <- model.matrix(~ 1 + x1)
K <- ncol(X)
model_data <- list(Y = y, X = X, K = K, N = nobs,
Zeros = rep(0, nobs))

LNORM <-"
model{
# Diffuse normal priors for predictors
for (i in 1:K) { beta[i] ~ dnorm(0, 0.0001) }

# Uniform prior for standard deviation
tau <- pow(sigma, -2)                                              # precision
sigma ~ dunif(0, 100)                                              # standard deviation

# Likelihood
for (i in 1:N){
Y[i] ~ dlnorm(mu[i],tau)
mu[i] <- eta[i]
eta[i] <- inprod(beta[], X[i,])
}
}"

inits <- function () { list(beta = rnorm(K, 0, 0.01)) }

params <- c("beta", "sigma")

LN <- jags(data = model_data,
inits = inits,
parameters = params,
model = textConnection(LNORM),
n.chains = 3,
n.iter = 5000,
n.thin = 1,
n.burnin = 2500)

print(LN, intervals=c(0.025, 0.975), digits=3)

==================================================

out <- LN\$BUGSoutput
MyBUGSHist(out,c(uNames("beta",K),"sigma"))

MyBUGSChains(out,c(uNames("beta",K),"sigma")) Output on screen:

Inference for Bugs model at "3", fit using jags,

3 chains, each with 5000 iterations (first 2500 discarded)

n.sims = 7500 iterations saved

mu.vect      sd.vect          2.5%             97.5%        Rhat       n.eff

beta                 1.994       0.028          1.940               2.048      1.002       2200

beta                 3.005      0.048           2.911               3.099      1.001       4700

sigma                   0.999      0.010          0.980                1.019      1.001       7500

deviance      49162.565      2.419  49159.819        49168.725      1.000             1

For each parameter, n.eff is a crude measure of effective sample size,

and Rhat is the potential scale reduction factor (at convergence, Rhat=1).

DIC info (using the rule, pD = var(deviance)/2)

pD = 2.9 and DIC = 49165.5

DIC is an estimate of expected predictive error (lower deviance is better).  