The marginal likelihood for parameters in a discrete Gauss-Markov process

We use Laplaceʹs method to approximate the marginal likelihood for parameters in a Gauss–Markov process. This approximation requires the determinant of a matrix whose dimensions are equal to the number of state variables times the number of time points. We reduce this to sequential evaluation of determinants and inverses of smaller matrices. We show this is a numerically stable method.