We introduce the Gaussian orthogonal latent factor processes for modeling and predicting large correlated data. To handle the computational challenge, we first decompose the likelihood function of the Gaussian random field with multi-dimensional input domain into a product of densities at the orthogonal components with lower dimensional inputs. The continuous-time Kalman filter is implemented to efficiently compute the likelihood function without making approximation. We also show that the posterior distribution of the factor processes are independent, as a consequence of prior independence of factor processes and orthogonal factor loading matrix. For studies with a large sample size, we propose a flexible way to model the mean in the model and derive the closed-form marginal posterior distribution. Both simulated and real data applications confirm the outstanding performance of this method.

翻译：我们引入了用于模拟和预测大相关数据的高斯正方位潜在系数进程。 为了处理计算挑战, 我们首先将高斯随机字段具有多维输入域的可能性功能分解为具有低维输入的正方位组件密度的产物。 连续时间 Kalman 过滤器的安装是为了高效计算概率函数, 而不做近光线。 我们还显示, 系数过程的后端分布是独立的, 因为先前要素进程和正方位要素装载矩阵是独立的。 对于具有大样本规模的研究, 我们提出一种灵活的方法来模拟模型中的平均值, 并得出封闭式边端外层分布。 模拟和真实数据应用都证实了这一方法的杰出性能 。