Inference and control of the nosocomial transmission of methicillin-resistant Staphylococcus aureus

Pei, Sen; Morone, Flaviano; Liljeros, Fredrik; Makse, Hernán; Shaman, Jeffrey L

To represent the state-space distribution, the EAKF maintains an ensemble of system state vectors acting as samples from the distribution. In particular, the EAKF assumes that both the prior distribution and likelihood are Gaussian, and thus can be fully characterized by their first two moments, that is mean and covariance. The update scheme for ensemble members is computed using Bayes' rule (posterior / prior  likelihood) via the convolution of the two Gaussian distributions. For observed state variables, the posterior of the i th ensemble member is updated through are the variances of the observation and the prior observed variable; and o t is the observation at time t. Unobserved variables and parameters are updated through their covariability with the observed variable, which can be computed directly from the ensemble. In particular, the i th ensemble member of unobserved variable or parameter x i is updated by