| Statistical Programs |
| College of Agriculture | University of Idaho |
| Seminar Announcement |
| "Applied Statistics in Agriculture" |
|
Estimating Observation Error, Process Noise,
and Density Dependence
Presented By |
| Dr. Brian C. Dennis |
|
Department of Fish and Wildlife Resources and Division of Statistics University of Idaho |
| Tuesday, April 15 3:30 P. M. Ag. Science 62 |
|
A standing problem in population ecology is how to estimate
parameters in stochastic population models that incorporate both observation (or sampling)
error and process noise. Promising "state space" formulations have been proposed, but it
is fair to say that such models to date have not attained widespread usage in population
ecology. The models have been either too simple biologically, as with the linear Gaussian
("Kalman filter") model, or too statistically and computationally advanced for routine use
by biologists. Furthermore, with the biologically realistic models, investigators who have
undertaken the enormous computations for simulations commonly report problems with biases,
multimodal or flat likelihoods, estimability, and parameter confounding, leaving the
interpretation of data analyses with such models somewhat unsettled. I will present a state space population model that retains some biological realism, yet is fairly easy to use. The model is a stochastic, discrete time, Gompertz growth model with environmental-type process error and lognormal sampling error. The Gompertz is a model of density dependent population growth that has held its own in many comparative model-fitting studies of population time series data. The lognormal sampling error embodies the features of many standard ecological sampling methods. The resulting nonlinear state space model can be transformed into the linear Gaussian model that has easy formulas and straightforward computing. A multivariate normal likelihood yields ML parameter estimates via simple numerical maximization. Example analyses with the model shed light on the estimation problems that occur in the more complex models. Parameter estimates with improved statistical properties can be obtained by differencing the data, a procedure akin to REML estimation in random effects models. |
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