  We report an exact likelihood computation for Linear Gaussian Markov
processes that is more scalable than existing algorithms for complex models and
sparsely sampled signals. Better scaling is achieved through elimination of
repeated computations in the Kalman likelihood, and by using the diagonalized
form of the state transition equation. Using this efficient computation, we
study the accuracy of kernel learning using maximum likelihood and the
posterior mean in a simulation experiment. The posterior mean with a reference
prior is more accurate for complex models and sparse sampling. Because of its
lower computation load, the maximum likelihood estimator is an attractive
option for more densely sampled signals and lower order models. We confirm
estimator behavior in experimental data through their application to speleothem
data.
