ABSTRACT
The design-based and model-based approaches to frequentist statistical inference rest on fundamentally different foundations. In the design-based approach, inference relies on random sampling. In the model-based approach, inference relies on distributional assumptions. We compare the approaches in a finite population spatial context.We provide relevant background for the design-based and model-based approaches and then study their performance using simulated data and real data. The real data is from the United States Environmental Protection Agency's 2012 National Lakes Assessment. A variety of sample sizes, location layouts, dependence structures, and response types are considered. The population mean is the parameter of interest, and performance is measured using statistics like bias, squared error, and interval coverage.When studying the simulated and real data, we found that regardless of the strength of spatial dependence in the data, the generalized random tessellation stratified (GRTS) algorithm, which explicitly incorporates spatial locations into sampling, tends to outperform the simple random sampling (SRS) algorithm, which does not explicitly incorporate spatial locations into sampling. We also found that model-based inference tends to outperform design-based inference, even for skewed data where the model-based distributional assumptions are violated. The performance gap between design-based inference and model-based inference is small when GRTS samples are used but large when SRS samples are used, suggesting that the sampling choice (whether to use GRTS or SRS) is most important when performing design-based inference.There are many benefits and drawbacks to the design-based and model-based approaches for finite population spatial sampling and inference that practitioners must consider when choosing between them. We provide relevant background contextualizing each approach and study their properties in a variety of scenarios, making recommendations for use based on the practitioner's goals.
ABSTRACT
Harbor seals in Iliamna Lake, Alaska, are a small, isolated population, and one of only two freshwater populations of harbor seals in the world, yet little is known about their abundance or risk for extinction. Bayesian hierarchical models were used to estimate abundance and trend of this population. Observational models were developed from aerial survey and harvest data, and they included effects for time of year and time of day on survey counts. Underlying models of abundance and trend were based on a Leslie matrix model that used prior information on vital rates from the literature. We developed three scenarios for variability in the priors and used them as part of a sensitivity analysis. The models were fitted using Markov chain Monte Carlo methods. The population production rate implied by the vital rate estimates was about 5% per year, very similar to the average annual harvest rate. After a period of growth in the 1980s, the population appears to be relatively stable at around 400 individuals. A population viability analysis assessing the risk of quasi-extinction, defined as any reduction to 50 animals or below in the next 100 years, ranged from 1% to 3%, depending on the prior scenario. Although this is moderately low risk, it does not include genetic or catastrophic environmental events, which may have occurred to the population in the past, so our results should be applied cautiously.
