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A conditional autoregressive Gaussian process for irregularly spaced multivariate data with application to modelling large sets of binary data

机译:不规则空间多元数据的条件自回归高斯过程及其在建模大型二进制数据中的应用

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A Gaussian conditional autoregressive (CAR) formulation is presented that permits the modelling of the spatial dependence and the dependence between multivariate random variables at irregularly spaced sites so capturing some of the modelling advantages of the geostatistical approach. The model benefits not only from the explicit availability of the full conditionals but also from the computational simplicity of the precision matrix determinant calculation using a closed form expression involving the eigenvalues of a precision matrix submatrix. The introduction of covariates into the model adds little computational complexity to the analysis and thus the method can be straightforwardly extended to regression models. The model, because of its computational simplicity, is well suited to application involving the fully Bayesian analysis of large data sets involving multivariate measurements with a spatial ordering. An extension to spatio-temporal data is also considered. Here, we demonstrate use of the model in the analysis of bivariate binary data where the observed data is modelled as the sign of the hidden CAR process. A case study involving over 450 irregularly spaced sites and the presence or absence of each of two species of rain forest trees at each site is presented; Markov chain Monte Carlo (MCMC) methods are implemented to obtain posterior distributions of all unknowns. The MCMC method works well with simulated data and the tree biodiversity data set.
机译:提出了一种高斯条件自回归(CAR)公式,该模型允许对空间依存关系以及不规则间隔位置处的多元随机变量之间的依存关系进行建模,从而获得了地统计方法的一些建模优势。该模型不仅受益于全部条件的显式可用性,而且受益于使用涉及精确矩阵子矩阵特征值的闭式表达式进行的精确矩阵行列式计算的计算简单性。在模型中引入协变量不会增加分析的计算复杂度,因此该方法可以直接扩展到回归模型。该模型由于其计算简单性,非常适合涉及对大型数据集进行完全贝叶斯分析的应用程序,该分析涉及具有空间顺序的多变量测量。还考虑了时空数据的扩展。在这里,我们演示了该模型在二元二进制数据分析中的使用,其中将观察到的数据建模为隐藏CAR过程的标志。提出了一个案例研究,涉及450多个不规则间隔的地点,每个地点是否存在两种雨林树;实施马尔可夫链蒙特卡罗(MCMC)方法以获得所有未知数的后验分布。 MCMC方法适用于模拟数据和树木生物多样性数据集。

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