Non-Gaussian spatiotemporal modelling through scale mixing
Non-Gaussian spatiotemporal modelling through scale mixing
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DOI：
10.1093/biomet/asr047
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发表时间：
2011-12-01
期刊：
影响因子：
2.7
通讯作者：
Steel, Mark F. J.
中科院分区：
文献类型：
--
作者：
Fonseca, Thais C. O.;Steel, Mark F. J.
我们构造了非高斯过程，在空间和时间上连续变化，具有不可分离的协方差函数。从一个通用的和灵活的方式构建有效的不可分离的协方差函数，通过混合可分离的协方差函数，所得到的模型一般化，允许离群值以及具有较大方差的区域。我们通过尺度混合与单独的正值过程诱导这一点。平滑混合过程应用于空间和时间上的潜在相关过程，从而导致空间和时间上的区域扩散增加。一个不相关的混合过程的块金效应容纳离群值。这些模型的后验和预测贝叶斯推理是通过马尔可夫链蒙特卡罗采样器实现的。在巴斯克地区的温度数据的应用程序说明了该模型在识别异常值和膨胀的方差区域的潜力，并表明，这提高了预测性能。
We construct non-Gaussian processes that vary continuously in space and time with nonseparable covariance functions. Starting from a general and flexible way of constructing valid nonseparable covariance functions through mixing over separable covariance functions, the resulting models are generalized by allowing for outliers as well as regions with larger variances. We induce this through scale mixing with separate positive-valued processes. Smooth mixing processes are applied to the underlying correlated processes in space and in time, thus leading to regions in space and time of increased spread. An uncorrelated mixing process on the nugget effect accommodates outliers. Posterior and predictive Bayesian inference with these models is implemented through a Markov chain Monte Carlo sampler. An application to temperature data in the Basque country illustrates the potential of this model in the identification of outliers and regions with inflated variance, and shows that this improves the predictive performance.