A comparison of design-based and model-based approaches for finite population spatial sampling and inference

Area of Science:

• Environmental Science
• Statistics
• Spatial Analysis

Background:

• Frequentist statistical inference uses design-based (random sampling) and model-based (distributional assumptions) approaches.
• Finite population spatial contexts present unique challenges for both inference methods.

Purpose of the Study:

• To compare the performance of design-based and model-based inference in finite population spatial settings.
• To evaluate the impact of sampling strategies (GRTS vs. SRS) on inference accuracy.
• To analyze performance across various data scenarios, including spatial dependence and response types.

Main Methods:

• Utilized simulated and real-world data from the EPA's National Lakes Assessment (2012).
• Employed generalized random tessellation stratified (GRTS) and simple random sampling (SRS) algorithms.
• Assessed performance using bias, squared error, and interval coverage for population mean estimation.

Main Results:

• GRTS sampling consistently outperformed SRS, irrespective of spatial dependence strength.
• Model-based inference demonstrated superior performance compared to design-based inference, even with violated assumptions.
• The choice of sampling method (GRTS vs. SRS) significantly impacted the performance gap between design-based and model-based inference.

Conclusions:

• Model-based inference is recommended for spatial data analysis, even with potential distributional assumption violations.
• GRTS sampling is a crucial consideration for improving design-based inference in spatial contexts.
• Practitioners should carefully weigh the benefits and drawbacks of each approach based on their specific goals.