16.3 Notes on the EM algorithm

EM algorithms will quickly get in the vicinity of the maximum likelihood, but the final approach to the maximum is generally slow relative to quasi-Newton methods. On the flip side, EM algorithms are quite robust to initial conditions choices and can be extremely fast at getting close to the MLE values for high-dimensional models. The MARSS package also allows one to use the BFGS method to fit MARSS models, thus one can use an EM algorithm to get close and then the BFGS algorithm to polish off the estimate.

Restricted maximum-likelihood algorithms are also available for AR(1) state-space models, both univariate (Staples, Taper, and Dennis 2004) and multivariate (Hinrichsen and Holmes 2009). REML can give parameter estimates with lower variance than plain maximum-likelihood algorithms. Another maximum-likelihood method is data-cloning which adapts MCMC algorithms used in Bayesian analysis for maximum-likelihood estimation (Lele, Dennis, and Lutscher 2007).

Missing values are seamlessly accommodated with the EM algorithm in the MARSS package. Simply specify missing data with NAs. The likelihood computations are exact and will deal appropriately with missing values. However, no innovations, referring to the non-parametric bootstrap developed by Stoffer and Wall (1991), bootstrapping can be done if there are missing values. Instead parametric bootstrapping must be used.