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For spatial linear regression, the traditional approach to capture spatial dependence is to use a parametric linear mixed-effects model. Spline surfaces can be used as an alternative to capture spatial variability, giving rise to a semiparametric method that does not require the specification of a parametric covariance structure. The spline component in such a semiparametric method, however, impacts the estimation of the regression coefficients. In this paper, we investigate such an impact in spatial linear regression with spline-based spatial effects. Statistical properties of the regression coefficient estimators are established under the model assumptions of the traditional spatial linear regression. Further, we examine the empirical properties of the regression coefficient estimators under spatial confounding via a simulation study. A data example in precision agriculture research regarding soybean yield in relation to field conditions is presented for illustration.

We propose an interacting cluster model for the spatial distribution of epidermal nerve fibers (ENF). The model consists of a spatial process of parent points modeling the base points of nerve fiber bundles. To each base point there is an offspring point process of fibers end points associated. The parent process is, possibly, inhibited by fiber endings that belong to different base bundles. The fibers themselves have random length and spatial orientation. We consider a non-orphan process where we can connect each offspring to a parent. We examine the processes that can be described with our model, how coefficient estimation can be performed under the Bayesian paradigm via Markov chain Monte Carlo methods, and detail approaches for the implementation of efficient MCMC sampling schemes. We study the performance of the estimation procedure through a simulation study. An application to data from skin blister biopsy images of ENFs is presented.

Rapid technological advances have drastically improved the data collection capacity in occupational exposure assessment. However, advanced statistical methods for analyzing such data and drawing proper inference remain limited. The objectives of this paper are (1) to provide new spatio-temporal methodology that combines data from both roving and static sensors for data processing and hazard mapping across space and over time in an indoor environment, and (2) to compare the new method with the current industry practice, demonstrating the distinct advantages of the new method and the impact on occupational hazard assessment and future policy making in environmental health as well as occupational health. A novel spatio-temporal model with a continuous index in both space and time is proposed, and a profile likelihood-based model fitting procedure is developed that allows fusion of the two types of data. To account for potential differences between the static and roving sensors, we extend the model to have nonhomogenous measurement error variances. Our methodology is applied to a case study conducted in an engine test facility, and dynamic hazard maps are drawn to show features in the data that would have been missed by existing approaches, but are captured by the new method.