Intrinsic Gaussian Markov Random Fields (IGMRFs) can be used to induce conditional dependence in Bayesian hierarchical models. IGMRFs have both a precision matrix, which defines the neighbourhood structure of the model, and a precision, or scaling, parameter. Previous studies have shown the importance of selecting this scaling parameter appropriately for different types of IGMRF, as it can have a substantial impact on posterior results. Here, we focus on the two-dimensional case, where tuning of the parameter is achieved by mapping it to the marginal standard deviation of a two-dimensional IGMRF. We compare the effects of scaling various classes of IGMRF, including an application to blood pressure data using MCMC methods.

翻译：Intrinsic Gaussian Markov Random Fields(IGMRFs) 可用于诱导巴伊西亚等级模型的有条件依赖性。 IGMRFs 既有一个精确矩阵,界定模型的邻里结构,又有一个精确度或缩放参数。以前的研究表明,为不同类型IGMRF适当选择这一缩放参数的重要性,因为它可能对后方结果产生重大影响。这里,我们侧重于二维案例,通过对参数进行绘图,使其与二维IGMRF的边缘标准偏差相匹配,从而实现参数调控。我们比较了将各种类型IGMRF的缩放效应,包括使用MCM方法将血压数据应用到血压数据中。