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Exact Bayesian Geostatistics Under Preferential Sampling
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DOI：10.1214/24-BA1460.png)
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Abstract
En 中文
Preferential sampling is a common feature in geostatistics and occurs when the locations are sampled based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability law for the distribution of the locations. However, analytic intractability of the point process likelihood prevents its direct calculation. Many Bayesian (and non-Bayesian) approaches in non-parametric model specifications handle this difficulty with approximations, both to the model and to the computations required for drawing inference. Procedures to approximate the model lead to errors that are sometimes difficult to quantify and can lead to biased inference. This paper presents an approach for performing exact Bayesian inference for this setting without the need for model approximation. A qualitatively minor change on the traditional model is proposed to circumvent the likelihood intractability. This change enables the use of an augmented model strategy. Recent work on Bayesian inference for point pattern models can be adapted to the geostatistics setting and renders computational tractability for exact inference for the proposed methodology. Estimation of model parameters and prediction of the response at unsampled locations can then be obtained from the joint posterior distribution. Simulated studies showed good quality of the proposed model for estimation and prediction in a variety of scenarios. The performance of our approach is illustrated in the analysis of simulated and real datasets and also compares favourably against approximation-based approaches. The paper is concluded with comments regarding extensions and improvements to the proposed methodology.
Keywords:
Bayesian inference
data augmentation
geostatistics
point process
prediction
preferential sampling
Journal
IF:
2.5
Papers:
34
Citations:
3.0K
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