model{ y[1:s] ~ dmulti(th[1 : s] , n) sum.g <- sum(g[]) # smoothed frequencies for (i in 1 : s) { Sm[i] <- n * th[i] g[i] <- exp(gam[i]) th[i] <- g[i] / sum.g } # prior on elements of AR Precision Matrix rho ~ dunif(0, 1) tau ~ dunif(0.5, 10) # MVN for logit parameters gam[1 : s] ~ dmnorm(mu[], T[ , ]) for (j in 1:s) { mu[j] <- -log(s) } # Define Precision Matrix for (j in 2 : s - 1) { T[j, j] <- tau * (1 + pow(rho, 2)) } T[1, 1] <- tau T[s, s] <- tau for (j in 1 : s -1 ) { T[j, j + 1] <- -tau * rho T[j + 1, j] <- T[j, j + 1] } for (i in 1 : s - 1) { for (j in 2 + i : s) { T[i, j] <- 0; T[j, i] <- 0 } } # Or Could do in terms of covariance, which is simpler to write but slower # for (i in 1 : s) { # for (j in 1 : s) { # cov[i, j] <- pow(rho, abs(i - j)) / tau # } # } # T[1 : s, 1 : s] <- inverse(cov[ , ]) }