Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80888220181023Two Step Balanced Spatial Sampling Design for Prediction of Random FieldsTwo Step Balanced Spatial Sampling Design for Prediction of Random Fields1151372310.22055/jamm.2018.13723FAMohsenMohammadzadehDepartment of Statistics, Tarbiat Modares University, Tehran, Iran0000-0002-2361-6145RaminKhavarzadehDepartment of Statistics, Tarbiat Modares University, Tehran, Iran.Journal Article20160812Spatial statistics is the analytical science of spatial correlated data. In environmental fields of studies that deal with spatially correlated data due to their location in a given area, on the other hand, in the survey sampling it is assumed that the sample is taken from a population with independent units. This assumption is used at all stages of sampling, analysis and modeling. But when the units of the study population are correlated, the entire process, such as sampling methods and statistical process requires review and the entire process will be considering the correlation structure. In the classic sampling methods from a variable, when some covariates exist, then the balanced sampling is used for improving the quality of sample. In this paper, we introduce spatial balanced sampling design where the components of the spatial locations are considered as covariates. Then in an intensive simulation study Is shown that the kriging error induced by our sampling method is less than foe the other available methods. Finally, the application of the proposed method is shown in a real example.Spatial statistics is the analytical science of spatial correlated data. In environmental fields of studies that deal with spatially correlated data due to their location in a given area, on the other hand, in the survey sampling it is assumed that the sample is taken from a population with independent units. This assumption is used at all stages of sampling, analysis and modeling. But when the units of the study population are correlated, the entire process, such as sampling methods and statistical process requires review and the entire process will be considering the correlation structure. In the classic sampling methods from a variable, when some covariates exist, then the balanced sampling is used for improving the quality of sample. In this paper, we introduce spatial balanced sampling design where the components of the spatial locations are considered as covariates. Then in an intensive simulation study Is shown that the kriging error induced by our sampling method is less than foe the other available methods. Finally, the application of the proposed method is shown in a real example.https://jamm.scu.ac.ir/article_13723_6573a7fb3ccd6862ebc9c87083a58a23.pdf