  Bagging (i.e., bootstrap aggregating) involves combining an ensemble of
bootstrap estimators. We consider bagging for inference from noisy or
incomplete measurements on a collection of interacting stochastic dynamic
systems. Each system is called a unit, and each unit is associated with a
spatial location. A motivating example arises in epidemiology, where each unit
is a city: the majority of transmission occurs within a city, with smaller yet
epidemiologically important interactions arising from disease transmission
between cities. Monte Carlo filtering methods used for inference on nonlinear
non-Gaussian systems can suffer from a curse of dimensionality as the number of
units increases. We introduce bagged filter (BF) methodology which combines an
ensemble of Monte Carlo filters, using spatiotemporally localized weights to
select successful filters at each unit and time. We obtain conditions under
which likelihood evaluation using a BF algorithm can beat a curse of
dimensionality, and we demonstrate applicability even when these conditions do
not hold. BF can out-perform an ensemble Kalman filter on a coupled population
dynamics model describing infectious disease transmission. A block particle
filter also performs well on this task, though the bagged filter respects
smoothness and conservation laws that a block particle filter can violate.
