  Many real-world phenomena are naturally bivariate. This includes blood
pressure, which comprises systolic and diastolic levels. Here, we develop a
Bayesian hierarchical model that estimates these values and their interactions
simultaneously, using sparse data that vary substantially between countries and
over time. A key element of the model is a two-dimensional second-order
Intrinsic Gaussian Markov Random Field, which captures non-linear trends in the
variables and their interactions. The model is fitted using Markov chain Monte
Carlo methods, with a block Metropolis-Hastings algorithm providing efficient
updates. Performance is demonstrated using simulated and real data.
