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

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Code 10.3 Gaussian linear mixed model, in R using JAGS, for modeling the relationship between type Ia supernovae host galaxy mass and Hubble residuals

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library(R2jags)

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# Data
path_to_data = "https://raw.githubusercontent.com/astrobayes/BMAD/master/data/Section_10p2/HR.csv"

dat <- read.csv(path_to_data, header = T)

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# Prepare data to JAGS
nobs = nrow(dat)
obsx1 <- dat$LogMass
errx1 <- dat$e_LogMass
obsy <- dat$HR
erry <- dat$e_HR

type <- as.numeric(dat$Type)                                     # convert class to numeric flag 1 or 2

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jags_data <- list(
         obsx1 = obsx1,
         obsy = obsy,
         errx1 = errx1,
         erry = erry,
         K = 2,
         N = nobs,
         type = type)

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# Fit
NORM_errors <-" model{
    tau0 ~ dunif(1e-1,5)
    mu0 ~ dnorm(0,1)

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    # Diffuse normal priors for predictors
    for (j in 1:2){
        for (i in 1:K) {
            beta[i,j] ~  dnorm(mu0, tau0)
        }
    }

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    # Gamma prior for standard deviation
    tau ~ dgamma(1e-3, 1e-3)                                         # precision
    sigma <- 1 / sqrt(tau)                                                 # standard deviation

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    # Diffuse normal priors for true x
    for (i in 1:N){
        x1[i] ~ dnorm(0,1e-3)
    }

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    # Likelihood function
    for (i in 1:N){
        obsy[i] ~ dnorm(y[i],pow(erry[i],-2))
        y[i] ~ dnorm(mu[i],tau)
        obsx1[i] ~ dnorm(x1[i],pow(errx1[i],-2))

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        mu[i] <- beta[1,type[i]] + beta[2,type[i]] * x1[i]
    }
}"

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inits <- function () {
    list(beta = matrix(rnorm(4, 0, 0.01),ncol = 2))
}

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params0 <- c("beta", "sigma")

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# Run MCMC
NORM <- jags(
             data = jags_data,
             inits = inits,
             parameters = params0,
             model = textConnection(NORM_errors),
             n.chains = 3,
             n.iter = 40000,
             n.thin = 1,
             n.burnin = 15000)

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# Output
print(NORM,justify = "left", digits=3)

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