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Model Evaluation and Spatial Interpolation by Bayesian Combination of Observations with Outputs from Numerical Models
Author(s) -
Fuentes Montserrat,
Raftery Adrian E.
Publication year - 2005
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2005.030821.x
Subject(s) - ground truth , computer science , interpolation (computer graphics) , bayesian probability , data mining , air quality index , scale (ratio) , set (abstract data type) , multivariate interpolation , posterior probability , bayesian inference , prior probability , data set , spatial analysis , algorithm , machine learning , mathematics , statistics , meteorology , artificial intelligence , cartography , geography , motion (physics) , computer vision , bilinear interpolation , programming language
Summary Constructing maps of dry deposition pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, there are two main sources of information for dry deposition levels in the United States: one is pollution measurements at a sparse set of about 50 monitoring stations called CASTNet, and the other is the output of the regional scale air quality models, called Models‐3. A related problem is the evaluation of these numerical models for air quality applications, which is crucial for control strategy selection. We develop formal methods for combining sources of information with different spatial resolutions and for the evaluation of numerical models. We specify a simple model for both the Models‐3 output and the CASTNet observations in terms of the unobserved ground truth, and we estimate the model in a Bayesian way. This provides improved spatial prediction via the posterior distribution of the ground truth, allows us to validate Models‐3 via the posterior predictive distribution of the CASTNet observations, and enables us to remove the bias in the Models‐3 output. We apply our methods to data on SO 2 concentrations, and we obtain high‐resolution SO 2 distributions by combining observed data with model output. We also conclude that the numerical models perform worse in areas closer to power plants, where the SO 2 values are overestimated by the models.