# Spatial Statistics

### Spatial Statistics

Spatial Statistics is the study of spatially correlated data. Spatial data arises from a wide range of fields including mining/geology, geography, agriculture, meteorology, air quality, mapping, epidemiology, and imaging, such as satellite or biomedical images.  Analysis of spatial data accounts for statistical dependencies, accuracy and uncertainty. Statistical methods applied to spatial data will analyze distributions, patterns, processes, and predictions. Analytic methods can be frequentist and Bayesian. Future directions have incorporated a temporal component where spatial data is also measured over time. This produces high dimensional data that requires increased computing power and specialized models.

GIS - A common way spatial data is analyzed is using Geographic Information System. GIS is a way to manage, map, and integrate spatial location data. GIS helps individuals visualize and understand patterns, and relationships in geographic form. As a part of GIS, spatial analysis can be used to estimate and make predictions at geospatial locations.

Small area estimation – Small area estimation (SAE) is an area of spatial statistics that allows survey samplers to provide more reliable estimates for small geographic areas or domains, that have limited number of observations available i.e., small sample sizes. SAE can also be used to provide valid estimates for subpopulations of these small areas, such as age groups or race categories. Bayesian methods for SAE allow for the borrowing of information or “strength” across boundaries or from multiple data sources to provide more reliable estimates for the small areas.

Kriging – Kriging is a method of spatial interpolation where a set of sampled data points are used to estimate a variable continuously over a spatial field. It is essentially a weighted regression analysis, predicting each unsampled location using data from neighboring locations. From kriging, we can get a prediction surface as well as estimates of prediction error or uncertainty.

Our department faculty have developed some innovative methods and applications in these areas.

1. Smith, L. M., Stroup, W. W., & Marx, D. B. (2020). Poisson cokriging as a generalized linear mixed model. Spatial statistics. 35: 100399.
2. Kolovos, A., Smith, L. M., Schwab-McCoy, A., Gengler, S., & Yu, H. L. (2016). Emerging patterns in multi-sourced data modeling uncertainty. Spatial Statistics. 18: 300-317.
3. Samson, K. K., Haynatzki, G., Soliman, A. S., & Valerianova, Z. (2016). Temporal changes in the cervical cancer burden in Bulgaria: Implications for eastern european countries going through transition., Cancer epidemiology. 44:154-160.
4. Schmid K.K., Marx D., and Samal A. (2011). Weighted Bidimensional Regression. Geographical Analysis. 43(1): 1-13.
5. Lahiri, P., & Meza, J. L. (2006). Small area estimation. Encyclopedia of Environmetrics. 4.
6. Buskirk, T. D., & Meza, J. L. (2003). A Post-stratified Raking-ratio Estimator Linking National and State Survey Data for Estimating Drug Use. Journal of Official Statistics. 19(3): 237.
7. Meza, J. L. (2003). Empirical Bayes estimation smoothing of relative risks in disease mapping. Journal of Statistical Planning and Inference. 112(1-2): 43-62.