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We introduce Gaussian orthogonal latent factor processes for modeling andpredicting large correlated data. To handle the computational challenge, wefirst decompose the likelihood function of the Gaussian random field with  a multi-dimensional input domain into a product of densities at theorthogonal components with lower-dimensional inputs. The continuous-time Kalmanfilter is implemented to compute the likelihood function efficiently withoutmaking approximations. We also show that the posterior distribution of thefactor processes is independent, as a consequence of prior independence offactor processes and orthogonal factor loading matrix. For studies with largesample sizes, we propose a flexible way to model the mean, and we derive themarginal posterior distribution to solve identifiability issues in samplingthese parameters. Both simulated and real data applications confirm theoutstanding performance of this method.

Gaussian orthogonal latent factor processes for large incomplete matrices of correlated data