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.

翻译：许多现实世界现象是自然的两变现象。 这包括血压, 包括 systolic 和 distolic 等值。 在这里, 我们开发了一种贝叶斯等级模型, 利用各国间和一段时间内差异很大的稀少数据, 同时估算这些数值及其相互作用。 模型的一个关键要素是二维二阶的Intrinsic Gaussian Markov 随机字段, 它捕捉变量及其相互作用的非线性趋势。 该模型使用Markov 链 Monte Carlo 方法安装, 并配有块大都会- Hastings 算法, 提供有效的更新。 使用模拟和真实数据演示了性能 。