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 10.10 Beta model in R using JAGS, for accessing the relationship between the baryon fraction in atomic gas and galaxy stellar mass

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

require(R2jags)


# Data
path_to_data = "https://raw.githubusercontent.com/astrobayes/BMAD/master/data/Section_10p5/f_gas.csv"

# Read data
Fgas0 <-read.csv(path_to_data,header=T)

# Estimate F_gas
Fgas0$fgas <- Fgas0$M_HI/(Fgas0$M_HI+Fgas0$M_STAR)

# Prepare data to JAGS
N = nrow(Fgas0)
y <- Fgas0$fgas
x <- log(Fgas0$M_STAR,10)
X <- model.matrix(~ 1 + x)
K <- ncol(X)


beta_data <- list(Y = y,
                            X = X,
                            K = K,
                            N = N)

# Fit
Beta <-"model{
    # Diffuse normal priors for predictors
    for(i in 1:K){
        beta[i] ~ dnorm(0, 1e-4)
    }
    
    # Diffuse prior for theta
    theta~dgamma(0.01,0.01)

    # Likelihood function
    for (i in 1:N){
        Y[i] ~ dbeta(a[i],b[i])
        a[i] <- theta*pi[i]
        b[i] <- theta*(1-pi[i])
        logit(pi[i]) <- eta[i]

        eta[i] <- inprod(beta[],X[i,])
    }
}"

# Define initial values
inits <- function () {
  list(beta = rnorm(2, 0, 0.1),
        theta = runif(1,0,100))
}

# Identify parameters
params <- c("beta","theta")

Beta_fit <- jags(data = beta_data,
                           inits = inits,
                           parameters = params,
                           model = textConnection(Beta),
                           n.thin = 1,
                           n.chains = 3,
                           n.burnin = 5000,
                           n.iter = 7500)

# Output
print(Beta_fit,intervals=c(0.025, 0.975), justify = "left", digits=2)

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

Output on screen:

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

  3 chains, each with 7500 iterations (first 5000 discarded)

  n.sims = 7500 iterations saved

 

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

beta[1]              9.30           0.15            9.04             9.58        1.07         34

beta[2]            -0.98            0.01           -1.00           -0.95        1.07         34

theta               11.72            0.38          10.98           12.47       1.00       940

deviance   -2331.18            2.28     -2333.74      -2325.38       1.01       330

 

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 = 2.6 and DIC = -2328.6

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

© 2017 by Emille E. O. Ishida