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I have a question about potential bias for estimating abundance when fitting a homogeneous point process model to data generated by a non-uniform process. I will present 2 different examples. First, consider a situation where you are interested in realized abundance over a given region S (i.e., the state space) and design a study that places detectors evenly and throughout a region R that coincides with S (R = S). In simulations where the distribution of individual across the landscape was patchy, Efford and Fewster (2013) found that a homogeneous Poisson model could estimate N without substantial bias. For the second example, consider density is inhomogeneous, R is represented by an array of detector clusters and is a subset of S, and a homogeneous model is used. Am I correct stating that the potential bias of the estimate of realized N in this case would be very sensitive to the distribution of clusters? I assume that clusters would need to be stratified by ‘local’ differences in density if a homogeneous model was fitted because misrepresentation of areas with different densities in the sample would result in a biased estimate of the point intensity parameter which would bias an estimate of N for the entire region S. Obviously, explicitly modeling spatial variation in density as a function of landscape variables believed to be driving density would be preferred. However, I’m just trying to understand all the consequences of not having that information available and having to fit a homogeneous model.

Thanks
Jared

Jared

The real distinction is between design-based and model-based inference about the number or density in region S (by the way - calling that the "state space" confuses things - it may or may not be the region of integration, and my statistician friends roll their eyes at the use of "state space" in SECR). Distance sampling books and De Gruijter et al. 2006 have lots on the distinction.

Design-based inference applies whenever detectors have been placed according to a probability-based sampling design across the region of interest, even if detectors are clustered. My intuition, which probably coincides with yours, is that clustering of detectors will result in increased sampling variance if the true pattern is highly inhomogeneous (Efford & Fewster did not investigate this). "Bias" is a property of the estimator, which may still be zero. 'Stratification' is a concept within probability-based sampling.

Model-based inference is less secure and depends on model validity. I don't think you can say it is 'obviously' better, but it may be. Perhaps you can cover yourself by presenting the results as model-based predictions rather than 'estimates'.

Murray