Bayesian inference for generalized additive mixed models based on Markov random field priors
Bayesian inference for generalized additive mixed models based on Markov random field priors
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DOI：
10.1111/1467-9876.00229
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发表时间：
2001-01-01
影响因子：
1.6
通讯作者：
Lang, S
中科院分区：
文献类型：
--
作者：
Fahrmeir, L;Lang, S
在实践中，大多数回归问题需要灵活的半参数形式的预测模型的依赖关系的响应协变量。此外，经常需要添加随机效应，以解释由未观察到的异质性或纵向或空间数据中的相关性引起的过度分散。在广义加性和半参数混合模型中，我们提出了一个统一的贝叶斯推理方法，通过马尔可夫链Monte Carte模拟。不同类型的协变量，如通常的协变量与固定效应，计量协变量与非线性效应，非结构化的随机效应，趋势和季节性成分的纵向数据和空间协变量，都在同一个一般框架内进行处理，通过分配适当的马尔可夫随机场先验不同的形式和程度的光滑。我们在几个案例研究和咨询案例中应用了这种方法，表明该方法在具有许多协变量和大数据集的问题中也是计算可行的。在本文中，我们选择了两个典型的应用。
Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carte simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with fixed effects, metrical covariates with non-linear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates, are all treated within the same general framework by assigning appropriate Markov random field priors with different forms and degrees of smoothness. We applied the approach in several case-studies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications.