Applied Bayesian Modelling, 2nd Edition

Notes

1  These data kindly provided by Peyton Cook.

2  The code for this model assumes that in the program are the three latent data values , with [4] to [83] corresponding to the actual observations for 1909−1988. The code is

model { # outlier model for (t in 4:T + 3) { delta[t] ˜ dbern(Delta) eta[t] ˜ dnorm(0,tau.eta) o[t] <- eta[t]*delta[t]} Delta ˜ dbeta(1,19); tau.eta <- tau.G/10 # main model for (t in 4:T + 3) { y[t] ˜ dnorm(m[t],tau[t]) y.new[t] ˜ dnorm(m[t],tau[t]) e[t] <- pow(y[t]-y.new[t],2) # weights for scale mixture w[t] ˜ dgamma(nu.2,nu.2) tau[t] <- w[t]*tau.G; m[t] <- mu + o[t] + lambda*t + rho*(y[t-1]-o[t-1]) + phi[1]*(y[t-1]-y[t-2]) + phi[2]*(y[t-2]-y[t-3]) # log likelihood and inverse likelihood LL[t] <- 0.5*log(tau[t]/6.28)-0.5*tau[t] *pow(y[t]—m[t],2) # CPO estimated by inverse of posterior average of InvLk[] InvLk[t] <- 1/exp(LL[t])} # one step ahead predictions for (t in 5:T + 3) { m.p[t-1] <- m[t-1] + lambda y.one[t] ˜ dnorm(m.p[t-1],tau[t]) e2.one[t] <-pow(y[t]-y.one[t],2)} # assess stationarity NSTAT <- step(rho-1) # Predictive error E[1] <- sum(e2.one[5:T ...