| Statistical Programs |
| College of Agriculture and Life Sciences |
University of Idaho |
| Seminar Announcement |
| "Applied Statistics in Agriculture" |
|
Estimating Denisty Dependence, Process Noise, and Observation Error
Presented By |
| Dr. Brian C. Dennis |
|
Department of Fish and Wildlife Resources and Department of Statistics University of Idaho |
| Tuesday, November 9 3:30 P. M. Ag. Science 62 |
|
In this presentation I will describe a discrete time, stochastic population model
with density dependence, environmental-type process noise and lognormal observation or sampling error. The model, a
stochastic version of the Gompertz model, can be transformed into a linear Gaussian state space model (Kalman filter)
for convenient fitting to time series data. The model has a multivariate normal likelihood function and is simple
enough for a variety of uses ranging from theoretical study of parameter estimation issues to routine data analyses in
population monitoring. A special case of the model is the discrete time, stochastic exponential growth model (density
independence) with environmental-type process error and lognormal observation error. Two methods for estimating parameters in the Gompertz state space model, maximum likelihood based on observations and restricted maximum likelihood based on first differences, are compared with computer simulations. Both offer adequate statistical properties. Because the likelihood function is identical to a repeated measures analysis of variance model with a random time effect, parameter estimates can be calculated using PROC MIXED of SAS. Data sets from the Breeding Bird Survey provide illustrative analyses. For one data set, the fitted model suggests that over 70 percent of the noise in the population's growth rate is due to observation error. The model describes the autocovariance properties of the data especially well. While observation error and process noise variance parameters can both be estimated from one time series, multimodal likelihood functions can and do occur. For data arising from the model, the statistically consistent parameter estimates do not necessarily correspond to the global maximum in the likelihood function. Maximization, simulation, and bootstrapping programs must accomodate the phenomenon of multimodal likelihood functions to produce statistically valid results. A preprint of a paper (coauthors Jose Ponciano, Subhash Lele, Mark Taper, David Staples) forthcoming in Ecological Monographs is available from Dr. Dennis (brian@uidaho.edu). All interested faculty, staff, and graduate students are invited to attend. |
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