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 10.14 Poisson model, in R using JAGS, for modeling the relation between globular  clusters population and host galaxy visual magnitude

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require(R2jags)
require(jagstools)

 

# Data
path_to_data = "https://raw.githubusercontent.com/astrobayes/BMAD/master/data/Section_10p7/GCs.csv"

 

# Read data
GC_dat = read.csv(file=path_to_data,header = T,dec=".")

 

# Prepare data to JAGS
N <- nrow(GC_dat)
x <- GC_dat$MV_T
y <- GC_dat$N_GC
X <- model.matrix(~ x, data=GC_dat)
K = ncol(X)

 

 

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

 

# Fit
model.pois <- "model{
    # Diffuse normal priors betas
    for (i in 1:K) { beta[i] ~ dnorm(0, 1e-5)}
    
    for (i in 1:N){
        # Likelihood
        eta[i]<-inprod(beta[], X[i,])
        mu[i] <- exp(eta[i])
        Y[i]~dpois(mu[i])
        
        # Discrepancy
        expY[i] <- mu[i] # mean
        varY[i] <- mu[i] # variance
        PRes[i] <- ((Y[i] - expY[i])/sqrt(varY[i]))^2
    }
    
    Dispersion <- sum(PRes)/(N-2)
}"

 

# Define initial values
inits <- function () {
    list(beta = rnorm(K, 0, 0.1))
}

 

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

 

# Start JAGS
pois_fit <- jags(data = JAGS_data ,
                          inits = inits,
                          parameters = params,
                          model = textConnection(model.pois),
                          n.thin = 1,
                          n.chains = 3,
                          n.burnin = 3500,
                          n.iter = 7000)

 

# Output
print(pois_fit , intervals=c(0.025, 0.975), digits=3)

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