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

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

you are kindly asked to include the complete citation if you used this material in a publication

Code 4.10 Normal linear model in R using JAGS and including errors in variables

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require(R2jags)

# Data
set.seed(1056)                                              # set seed to replicate example
nobs = 1000                                                 # number of obs in model

sdobsx <- 1.25

truex <- rnorm(nobs, 0, 2.5)                          # normal variable
errx <- rnorm(nobs, 0, sdobsx)
obsx <- truex + errx

beta1 <- -4
beta2 <- 7
sdy <- 1.25
sdobsy <- 2.5

erry <- rnorm(nobs, 0, sdobsy)
truey <- rnorm(nobs,beta1 + beta2*truex, sdy)
obsy <- truey + erry

K <- 2

model.data <- list(obsy = obsy,
obsx = obsx,
K = K,
errx = errx,
erry = erry,
N = nobs)

NORM_err <-" model{
# Diffuse normal priors for predictors
for (i in 1:K) { beta[i] ~ dnorm(0, 1e-3) }

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

# Diffuse normal priors for true x
for (i in 1:N){
x[i] ~ dnorm(0,1e-3)
}

# Likelihood
for (i in 1:N){
obsy[i] ~ dnorm(y[i],pow(erry[i],-2))
y[i] ~ dnorm(mu[i],tauy)
obsx[i] ~ dnorm(x[i],pow(errx[i],-2))
mu[i] <- beta+beta*x[i]
}
}"

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

# Parameter to display and save
params <- c("beta", "sigma")

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

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

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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             -4.069        0.135            -4.331            -3.806      1.007         620

beta               6.753       0.058             6.636              6.862      1.008         280

sigma                 1.547       0.177             1.191              1.901      1.009         240

deviance      5391.166     51.448       5292.204        5492.494       1.001      6200

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 = 1323.4 and DIC = 6714.5

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

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