Abstract
The paper deals with the matter of producing geographical domains estimates for a variable with a spatial pattern in presence of incomplete information about the population units location. The spatial distribution of the study variable and its eventual relations with other covariates are modeled by a geoadditive regression. The use of such a model to produce model-based estimates for some geographical domains requires all the population units to be referenced at point locations, however typically the spatial coordinates are known only for the sampled units. An approach to treat the lack of geographical information for non-sampled units is suggested: it is proposed to impose a distribution on the spatial locations inside each domain. This is realized through a hierarchical Bayesian formulation of the geoadditive model in which a prior distribution on the spatial coordinates is defined. The performance of the proposed imputation approach is evaluated through various Markov Chain Monte Carlo experiments implemented under different scenarios.
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Notes
Tuscany is partitioned in ten provinces: Massa-Carrara, Lucca, Pistoia, Prato, Firenze, Livorno, Pisa, Siena, Arezzo and Grosseto. Because of the smaller extension of Prato and Pistoia, we consider them as a unique area in our analysis.
Fig. 8 
Spatial distributions of the population units: a Inhomogeneous Poisson process on each Tuscan province, b real population of rain gauges located in the Tuscan catchment basins
The meteo-hydrological data recorded by the Tuscan monitoring network are available for download from the Regional Hydrologic Service (www.sir.toscana.it).
A catchment basin is an extent of land where surface water from rain and melting snow or ice converges to a single point at a lower elevation, usually the exit of the basin, where the waters join another waterbody, such as a river, lake, reservoir, estuary, wetland, sea, or ocean. Tuscany is composed by twelve catchment basins, five of which belong mainly or completely to the Tuscan territory: Toscana Nord, Serchio, Toscana Costa, Ombrone and Arno (divided in Arno Superiore, Arno Medio and Arno Inferiore). Because of the smaller extension of the basins Toscana Nord and Serchio, we consider them as a unique area in our analysis; on the other hand, because of the great extension of the Arno basin, we consider its three sub-areas separately.
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Bocci, C., Rocco, E. Estimates for geographical domains through geoadditive models in presence of incomplete geographical information. Stat Methods Appl 23, 283–305 (2014). https://doi.org/10.1007/s10260-014-0256-9
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DOI: https://doi.org/10.1007/s10260-014-0256-9