This paper reviews the Kalman filter, which is a linear, minimum variance, sequential, model-based, time-series estimator based on the simple composite estimator. The Kalman filter combines predictions from a population dynamics model with the observed time-series of annual FIA panel estimates. This combination of design-based and model-based methods reduces serious risks from model bias, yet preserves the gain in precision from the model. Alternative models in the Kalman filter represent alternative hypotheses that may be ranked based on their relative agreement with design-based panel estimates. For example, does a model that includes the expected consequences of climate change on average rates of tree growth, regenerations and mortality better fit the annual FIA design-based panel estimates than a model that assumes no climate change?
The Kalman filter is presented in a tutorial style that relies more on graphical examples than mathematical equations. Hopefully, this genre builds awareness and confidence in this somewhat unfamiliar statistical estimator. The Kalman filter and Moving Average estimators are compared with hypothetical simulations of changing populations. A final set of examples is based on annual FIA panel estimates for the State of Colorado from 2002 to 2007, where epidemic levels of mountain pine beetle infestation are causing catastrophic tree mortality in lodgepole pine forests.
Three analysis questions are addressed. Is there an observable trend in population parameters over time? Does the trend make sense? Is the trend significant relative to the uncertainty in the population estimates?