  We introduce 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
  a 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 compute the likelihood function efficiently without
making approximations. We also show that the posterior distribution of the
factor processes is independent, as a consequence of prior independence of
factor processes and orthogonal factor loading matrix. For studies with large
sample sizes, we propose a flexible way to model the mean, and we derive the
marginal posterior distribution to solve identifiability issues in sampling
these parameters. Both simulated and real data applications confirm the
outstanding performance of this method.
