This section introduces models related to spatial sampling and statistical inference to help users understand functionality and select appropriate sampling models.
Single Point Local Estimation (SPA)
A method for unbiased estimation of population mean using a single valid sample point with full-coverage covariates strongly correlated to the target variable. When covariates show strong correlation with the study object, this model achieves unbiased estimation of the population.
BShade Model
A method for unbiased estimation using biased samples by calculating association coefficients between samples through existing data or covariates. It significantly improves estimation accuracy when sufficient historical data or prior information can quantify sample-to-population ratios and intra-population covariance.
Simple Random Sampling
Selects n sampling units from a population where all possible combinations have equal probability. Suitable for homogeneous populations without spatial correlation. Use Moran’s I statistic and Geographic Detector q-value to assess spatial correlation and heterogeneity.
System Random Sampling
Selects samples at fixed intervals from ordered population units. More practical than simple random sampling while maintaining uniform spatial distribution.
Spatial Simple Random Sampling
Incorporates spatial autocorrelation in sample size calculation and statistical inference. Requires fewer samples than simple random sampling for equivalent precision. Effective for spatially autocorrelated but homogeneous populations.
Stratum Random Sampling
Independently samples from population strata (n=n1+n2+...+nL). Superior for heterogeneous populations with distinct inter-strata differences and low intra-strata variation. Suitable for spatially heterogeneous but non-autocorrelated objects.
Spatial Stratification Random Sampling
Combines spatial stratification with autocorrelation considerations. Groups spatial units into layers with minimized intra-layer variance and maximized inter-layer variance. Particularly effective for complex populations with significant spatial heterogeneity and correlation.
Sandwich Random Sampling
Adds reporting unit layers (e.g., administrative/natural units) to spatial stratification. Enables multi-unit reporting with minimal samples. Ideal for strongly differentiated populations requiring small-sample multi-unit reporting.
The following figure shows an application diagram of sandwich random sampling:
The table below summarizes model definitions and characteristics for spatial sampling and statistical inference:
| Model Name | Description | Features |
|---|---|---|
| Simple Random Sampling | Completely random selection without stratification or ordering | Equal selection probability, independent units. Foundation for other sampling methods |
| System Random Sampling | Selection at fixed intervals from ordered population | Uniform distribution, smaller sample size than pure random sampling |
| Stratum Random Sampling | Independent sampling from heterogeneous strata | Improved precision through variance minimization within strata |
| Spatial Simple Random Sampling | Simple random sampling with spatial autocorrelation | Smaller sample size, higher efficiency through autocorrelation |
| Spatial Stratification Random Sampling | Stratified sampling with spatial autocorrelation | Higher precision than standard stratification with fewer samples |
| Sandwich Random Sampling | Multi-layer reporting unit integration | Enables multi-unit reporting with minimal samples |
| Single Point Local Estimation (SPA) | Unbiased estimation from single sample with covariates | Optimal solution for single-sample scenarios |
| BShade Model | Bias correction using spatial associations | Essential for biased samples with missing strata data |
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