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Many real-world phenomena are naturally bivariate. This includes bloodpressure, which comprises systolic and diastolic levels. Here, we develop aBayesian hierarchical model that estimates these values and their interactionssimultaneously, using sparse data that vary substantially between countries andover time. A key element of the model is a two-dimensional second-orderIntrinsic Gaussian Markov Random Field, which captures non-linear trends in thevariables and their interactions. The model is fitted using Markov chain MonteCarlo methods, with a block Metropolis-Hastings algorithm providing efficientupdates. Performance is demonstrated using simulated and real data.

A Two-Dimensional Intrinsic Gaussian Markov Random Field for Blood Pressure Data