Bayesian inference for finite populations under spatial process settings

Chan‐Golston, Alec M.; Banerjee, Sudipto; Handcock, Mark S.

doi:10.1002/env.2606

Cited by 7 publications

(6 citation statements)

References 40 publications

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“…Cooper (2006) reviews the two approaches in an ecological context before introducing a 'model-assisted' variance estimator that combines aspects from each approach. In addition to Cooper (2006), there has been substantial research and development into estimators that use both design-based and model-based principles (see e.g., Sterba (2009) and Cicchitelli and Montanari (2012), and for Bayesian approaches, see Chan-Golston et al (2020) and Hofman and Brus (2021)).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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1. 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.2. 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 are 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.3. 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.4. 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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2022

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“…Recent work includes a method for block kriging which connects geostatistical models and classical design-based sampling (Hoef, 2002), a spline-based estimator of the mean for samples drawn from a spatially-correlated population (Cicchitelli & Montanari, 2012), and the use of linear spatial interpolator to create a design-based predictor of values at unobserved locations (Bruno et al, 2013). Chan-Golston et al (2020) demonstrated that accounting for both design and spatial association in a two-stage sampling context led to better model fit and better coverage of the finitepopulation parameters.…”

Section: Introductionmentioning

confidence: 99%

Bayesian finite-population inference with spatially correlated measurements

Chan‐Golston

Banerjee²,

Belin³

et al. 2022

Jpn J Stat Data Sci

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Community-based public health interventions often rely on representative, spatially referenced outcome data to draw conclusions about a finite population. To estimate finite-population parameters, we are posed with two challenges: to correctly account for spatial association among the sampled and nonsampled participants and to correctly model missingness in key covariates, which may be also spatially associated. To accomplish this, we take inspiration from the preferential sampling literature and develop a general Bayesian framework that can specifically account for preferential non-response. This framework is first applied to three missing data scenarios in a simulation study. It is then used to account for missing data patterns seen in reported annual household income in a corner-store intervention project. Through this, we are able to construct finite-population estimates of the percent of income spent on fruits and vegetables. Such a framework provides a flexible way to account for spatial association and complex missing data structures in finite populations.

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“…To illustrate, we turn to nitrate concentration data collected in wells in California. Note that these data are discussed and analyzed more thoroughly in Section 5 and similar data were analyzed in Chan-Golston et al (2020). The population data consist of approximately 7000 wells in central California.…”

Section: Introductionmentioning

confidence: 99%

Correcting spatial Gaussian process parameter and prediction variance estimation under informative sampling

Schliep,

Wikle,

Daw

2021

Preprint

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Informative sampling designs can impact spatial prediction, or kriging, in two important ways. First, the sampling design can bias spatial covariance parameter estimation, which in turn can bias spatial kriging estimates. Second, even with unbiased estimates of the spatial covariance parameters, since the kriging variance is a function of the observation locations, these estimates will vary based on the sample and overestimate the population-based estimates. In this work, we develop a weighted composite likelihood approach to improve spatial covariance parameter estimation under informative sampling designs. Then, given these parameter estimates, we propose three approaches to quantify the effects of the sampling design on the variance estimates in spatial prediction. These results can be used to make informed decisions for population-based inference. We illustrate our approaches using a comprehensive simulation study. Then, we apply our methods to perform spatial prediction on nitrate concentration in wells located throughout central California.

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Bayesian inference for finite populations under spatial process settings

Cited by 7 publications

References 40 publications

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

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

Bayesian finite-population inference with spatially correlated measurements

Correcting spatial Gaussian process parameter and prediction variance estimation under informative sampling

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