Bayesian area-to-point kriging using expert knowledgeas informative priors

Abstract

Area-to-point (ATP) kriging is a common geostatistical framework to address the problem of spatial dis-aggregation or downscaling from block support observations (BSO) to point support (PoS) predictions forcontinuous variables. This approach requires that the PoS variogram is known. Without PoS observations,the parameters of the PoS variogram cannot be deterministically estimated from BSO, and as a result, thePoS variogram parameters are uncertain. In this research, we used Bayesian ATP conditional simulationto estimate the PoS variogram parameters from expert knowledge and BSO, and quantify uncertainty ofthe PoS variogram parameters and disaggregation outcomes. We first clarified that the nugget parame-ter of the PoS variogram cannot be estimated from only BSO. Next, we used statistical expert elicitationtechniques to elicit the PoS variogram parameters from expert knowledge. These were used as infor-mative priors in a Bayesian inference of the PoS variogram from BSO and implemented using a Markovchain Monte Carlo algorithm. ATP conditional simulation was done to obtain stochastic simulations atpoint support. MODIS (Moderate Resolution Imaging Spectroradiometer) atmospheric temperature pro-file data were used in an illustrative example. The outcomes from the Bayesian ATP inference for theMatérn variogram model parameters confirmed that the posterior distribution of the nugget parameterwas effectively the same as its prior distribution; for the other parameters, the uncertainty was substan-tially decreased when BSO were introduced to the Bayesian ATP estimator. This confirmed that expertknowledge brought new information to infer the nugget effect at PoS while BSO only brought new infor-mation to infer the other parameters. Bayesian ATP conditional simulations provided a satisfactory wayto quantify parameters and model uncertainty propagation through spatial disaggregation.