Using a Bayesian estimator to combine information from a cluster analysis and remote sensing data to estimate high-resolution data for agricultural production in Germany
In Germany, a county-resolution data set that consists of 35 land-use and animal-stock categories has been used extensively to assess the impact of agriculture on the environment. However, because such environmental effects as emission or nutrient surplus depend on the location, even a county resolution might produce misleading results. The aim of this article is to propose a Bayesian approach which combines two sorts of information, with one being treated as defining the prior and the other the data to form a posterior, used to estimate a data set at a municipality resolution. We define the joint prior density function based on (i) remote sensing data, thus accounting for differences in county data and missing data at the municipality level, and (ii) the results of a cluster analysis that was previously applied to the micro-census, whereas the data are defined by official statistics at the county level. This approach results in a fairly accurate data set at the municipality level. The results, using the proposed method, are validated by the national research data centre by comparing the estimates to actual observations. The test statistics presented here demonstrate that the proposed approach adequately estimates the production activities.