Model-based geostatistics from a Bayesian perspective: Investigating area-to-point kriging with small datasets

L. Steinbuch, Thomas Orton, D.J. Brus

Research output: Contribution to conferencePosterAcademic

Abstract

Area-to-point kriging (ATPK) is a geostatistical method for creating raster maps of high resolution using data of the variable ofinterest of much lower resolution. The dataset of areal means is often considerably smaller than the size of dataset conventionallydealt with in geostatistical analyses. In contemporary ATPK methods, uncertainty in the variogram parameters is not accounted forin the prediction; this issue can be overcome by applying ATPK in a Bayesian framework. Commonly in Bayesian statistics,posterior distributions of model parameters and posterior predictive distributions are approximated by Markov chain Monte Carlosampling from the posterior, which can be computationally expensive. We therefore implemented a partly analytical solution. Weused this implementation to (i) explore the impact of the prior distribution on predictions and prediction variances, (ii) investigatewhether certain aspects of uncertainty can be disregarded, simplifying the necessary computations, and (iii) test the impact ofvarious model misspecifications. We compared several approaches using simulated data, real-world point data that we aggregatedourselves, and a case study on aggregated crop yields in Burkina Faso. We found the prior distribution to have minimal impact onthe disaggregated predictions.We found that in most cases with known short-range behaviour, an approach that disregardeduncertainty in the variogram range parameter gave a reasonable assessment of prediction uncertainty. However, we found somesevere effects of model misspecification in terms of overly conservative or optimistic prediction uncertainties, highlighting the importance of model choice or integration in ATPK.

Conference

ConferenceWageningen Soil Conference 2019
CountryNetherlands
CityWageningen
Period27/08/1930/08/19

Fingerprint

geostatistics
kriging
prediction
variogram
raster
Markov chain
crop yield
distribution
parameter

Cite this

Steinbuch, L., Orton, T., & Brus, D. J. (2019). Model-based geostatistics from a Bayesian perspective: Investigating area-to-point kriging with small datasets. Poster session presented at Wageningen Soil Conference 2019, Wageningen, Netherlands.
Steinbuch, L. ; Orton, Thomas ; Brus, D.J. / Model-based geostatistics from a Bayesian perspective: Investigating area-to-point kriging with small datasets. Poster session presented at Wageningen Soil Conference 2019, Wageningen, Netherlands.
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Steinbuch, L, Orton, T & Brus, DJ 2019, 'Model-based geostatistics from a Bayesian perspective: Investigating area-to-point kriging with small datasets' Wageningen Soil Conference 2019, Wageningen, Netherlands, 27/08/19 - 30/08/19, .

Model-based geostatistics from a Bayesian perspective: Investigating area-to-point kriging with small datasets. / Steinbuch, L.; Orton, Thomas; Brus, D.J.

2019. Poster session presented at Wageningen Soil Conference 2019, Wageningen, Netherlands.

Research output: Contribution to conferencePosterAcademic

TY - CONF

T1 - Model-based geostatistics from a Bayesian perspective: Investigating area-to-point kriging with small datasets

AU - Steinbuch, L.

AU - Orton, Thomas

AU - Brus, D.J.

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N2 - Area-to-point kriging (ATPK) is a geostatistical method for creating raster maps of high resolution using data of the variable ofinterest of much lower resolution. The dataset of areal means is often considerably smaller than the size of dataset conventionallydealt with in geostatistical analyses. In contemporary ATPK methods, uncertainty in the variogram parameters is not accounted forin the prediction; this issue can be overcome by applying ATPK in a Bayesian framework. Commonly in Bayesian statistics,posterior distributions of model parameters and posterior predictive distributions are approximated by Markov chain Monte Carlosampling from the posterior, which can be computationally expensive. We therefore implemented a partly analytical solution. Weused this implementation to (i) explore the impact of the prior distribution on predictions and prediction variances, (ii) investigatewhether certain aspects of uncertainty can be disregarded, simplifying the necessary computations, and (iii) test the impact ofvarious model misspecifications. We compared several approaches using simulated data, real-world point data that we aggregatedourselves, and a case study on aggregated crop yields in Burkina Faso. We found the prior distribution to have minimal impact onthe disaggregated predictions.We found that in most cases with known short-range behaviour, an approach that disregardeduncertainty in the variogram range parameter gave a reasonable assessment of prediction uncertainty. However, we found somesevere effects of model misspecification in terms of overly conservative or optimistic prediction uncertainties, highlighting the importance of model choice or integration in ATPK.

AB - Area-to-point kriging (ATPK) is a geostatistical method for creating raster maps of high resolution using data of the variable ofinterest of much lower resolution. The dataset of areal means is often considerably smaller than the size of dataset conventionallydealt with in geostatistical analyses. In contemporary ATPK methods, uncertainty in the variogram parameters is not accounted forin the prediction; this issue can be overcome by applying ATPK in a Bayesian framework. Commonly in Bayesian statistics,posterior distributions of model parameters and posterior predictive distributions are approximated by Markov chain Monte Carlosampling from the posterior, which can be computationally expensive. We therefore implemented a partly analytical solution. Weused this implementation to (i) explore the impact of the prior distribution on predictions and prediction variances, (ii) investigatewhether certain aspects of uncertainty can be disregarded, simplifying the necessary computations, and (iii) test the impact ofvarious model misspecifications. We compared several approaches using simulated data, real-world point data that we aggregatedourselves, and a case study on aggregated crop yields in Burkina Faso. We found the prior distribution to have minimal impact onthe disaggregated predictions.We found that in most cases with known short-range behaviour, an approach that disregardeduncertainty in the variogram range parameter gave a reasonable assessment of prediction uncertainty. However, we found somesevere effects of model misspecification in terms of overly conservative or optimistic prediction uncertainties, highlighting the importance of model choice or integration in ATPK.

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Steinbuch L, Orton T, Brus DJ. Model-based geostatistics from a Bayesian perspective: Investigating area-to-point kriging with small datasets. 2019. Poster session presented at Wageningen Soil Conference 2019, Wageningen, Netherlands.