########################################################################

# Cauchy Distribution using 0's trick.

########################################################################

model

{

for(i in 1:n)

{

# Likelihood excluding pi in the denominator

lik[i] <- 1/(sigma*(1+((diff[i]-mu)/sigma)*((diff[i]-mu)/sigma)))

lam[i] <- -log(lik[i])+10000 # Add some large constant to make lam[i] > 0

zeros[i] <- 0

zeros[i] ~ dpois(lam[i]) # this likelihood is proportional to lik[i]

}

mu ~ dnorm(0, 0.000001) # approximates the improper prior

sigma ~ dgamma(0.001, 0.001) # approximates the improper prior

lsigma <-log(sigma)

}

# Initial values.

list( mu = 0, sigma=1 )

# Data

list(n = 15)

# Data

diff[]

-67

-48

END