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

# Cauchy Distribution. Mixture representation

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

model

{

for(i in 1:n)

{

diff[i] ~ dnorm(mu, tau[i]) # likelihood

tau[i] <- lambda[i]/exp(lsigma*2) # x|lambda ~N(mu,sigma^2/lambda)

lambda[i]~dgamma(0.5, 0.5) # lambda ~Gamma(0.5, 0,5)

}

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

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

sigma2 <- sigma*sigma

lsigma <- log(sigma)

}

# Initial values. Load below values for mu and lsigma and "gen inits" for lambda

list( mu = 0, sigma=1 )

# Data

list(n = 15)

# Data

diff[]

-67

-48

6

8

14

16

23

24

28

29

41

49

67

60

75

END