An application of spatio-temporal modeling to finite population abundance prediction
Spatio-temporal models can be used to analyze data collected atvarious spatial locations throughout multiple time points. However, even witha finite number of spatial locations, there may be a lack of resources to sampleevery spatial location at every time point. We develop a spatio-temporalfinite-population block kriging (ST-FPBK) method to predict a quantity ofinterest, such as a mean or total, across a finite number of spatial locations.This ST-FPBK predictor incorporates an appropriate variance reduction forsampling from a finite population. Through an application to moose surveysin the east-central region of Alaska, we show that the predictor has a substantiallysmaller standard error compared to a predictor from the purely spatialmodel that is currently used to analyze moose surveys in the region. We alsoshow how the model can be used to forecast a prediction for abundance ina time point for which spatial locations have not yet been surveyed. A separatesimulation study shows that the spatio-temporal predictor is unbiased and that prediction intervals from the ST-FPBK predictor attain appropriatecoverage. For ecological monitoring surveys completed with some regularitythrough time, use of ST-FPBK could improve precision. We also give an Rpackage that ecologists and resource managers could use to incorporate datafrom past surveys in predicting a quantity from a current survey.