Statistical methods for complex spatial data.

Spatial analysis is an active research area as it allows us to solve problems containing geographic information in various applications. In this dissertation, we consider some challenging issues we often face in practice. The work of this dissertation mainly focuses on spatial binary data. Binary data contains much less information than that of continuous type, which hinders our ability to obtain accurate predictions. To tackle this issue, we present a Bayesian downscaling model using spatially varying coefficients, which allows us to make inferences at high resolution from low resolution observed data. We also consider a situation where the binary data is measured with some errors, causing presence of misclassification in the data. In practice, misclassification is a well known problem, but often is ignored and analysis is performed as if data is measured perfectly. We address this issue by presenting a spatial misclassification model. While high resolution data may be superior in spatial coverage, it often suffers from a considerable number of censored observations due to a limit of detection of a device. To properly handle this issue, a statistical method with a predictor subject to censoring is presented. In addition, we relax a linearity assumption between a response and a predictor variable to increase the flexibility of modeling. We examine each model by performing extensive simulation studies and illustrate with real world applications using precipitation data in South Korea.