NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET

The objective of the study is to improve the robustness and flexibility of spatial kriging predictors with respect to deviations from spatial stationarity assumptions. A predictor based on a non-stationary Gaussian random field is defined. The model parameters are inferred in an empirical Bayesian setting, using observations in a local neighborhood and a prior model assessed from the global set of observations. The localized predictor appears with a shrinkage effect and is coined a localized/shrinkage kriging predictor. The predictor is compared to traditional localized kriging predictors in a case study on observations of annual cumulated precipitation. A crossvalidation criterion is used in the comparision. The shrinkage predictor appears as uniformly preferable to the traditional kriging predictors. A simulation study on prediction in non-stationary Gaussian random fields is conducted. The results from this study confirms that the shrinkage predictor is favorable to the traditional ones. Moreover, the crossvalidation criterion is found to be suitable for selection of predictor. Lastly, the shrinkage predictor appears as particularly robust towards spatially varying expectation functions. 1

Understanding the importance of spatial correlation in identifying spatio-temporal variation of disease risk, in the case of malaria risk mapping in southern Ethiopia

Malaria remains a major health problem in developing countries despite a significant reduction in incidence in the last few years. Disease mapping thus helps to understand the spatial pattern and identify areas characterized by unusual risks. Several spatial models have been used to analyze the incidence of malaria. We aim to compare the predictive performance of these models and investigate the effect of ignoring spatial correlation. The reported malaria case counts of genus P.falciparum in 149 districts of southern Ethiopia from January 2016 to May 2019 were analyzed using the spatial time series model (STS) that ignores spatial correlation, Spatio-temporal conditional autoregressive model (STCAR), Spatio-temporal geostatistical model (STG) and Spatio-temporal spatial discrete approximation to log Gaussian cox process (STSDALGCP). We assess the predictive performance of the models using root mean square error, mean absolute error, and coverage probability. We found that monthly average rainfall, temperature, humidity, and EVI are significantly associated with malaria risk. The spatial variation of malaria incidence changes with time, in particular, the high incidence was observed from November to December, months after heavy rainfall, and more pronounced in the southwest of the country. STSDALGCP gives a small prediction error in test set and captures the uncertainties better than other models, while the STS model gives a high prediction error. Accounting for spatial correlation is crucial for disease risk mapping and leads to better prediction of disease risk. Since malaria transmission operates in a spatially continuous manner, a spatially continuous model should be considered when it is computationally feasible.</p