modern_MVN_polynomial_model.jags

model
{

  ## MODERN DATA. likelihood
  for(i in 1:N.rows_m) {

    xrf_m[i,1:N.cols_m] ~ dmnorm(mean_m[i,1:N.cols_m], Sigma_inv)
    xrf_m_pred[i,1:N.cols_m] ~ dmnorm(mean_m[i,1:N.cols_m], Sigma_inv)

    for(j in 1:N.cols_m) {
      mean_m[i,j] <- beta0[j] + beta1[j]*NAO_m[i] + beta2[j]*pow(NAO_m[i],2)
    }  
  }

  # Prior on Sigma_inv
  Sigma_inv ~ dwish(R, k+1)

  ## Priors. One for each column (geochemical data)
  for (j in 1:N.cols_m) {
  
    beta0[j] ~ dnorm(0,10^-2)
    beta1[j] ~ dnorm(0,10^-2)
    beta2[j] ~ dnorm(0,10^-2)
    
  }#End loop priors

  ## Randow walk prior distribution for NAO modern
  for(i in 2:N.rows_m) { 
    NAO_m[i] ~ dnorm(NAO_m[i-1],prec_m[i])  
    prec_m[i] <- 1/((time_m[i]-time_m[i-1])*pow(sd_rw,2))
  }
  
  #Prior distribution for rw parameter
  sd_rw ~ dunif(0,20)

##End model
}