The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian variable selection based on spike-and-slab prior, bandwidth selection based on range prior, and model assessment using a modified deviance information criterion and a modified logarithm of pseudo-marginal likelihood are fully discussed in this paper. Usage of the graph distance in modeling areal data is also introduced. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods with both small and large number of location scenarios, and comparison with the classical frequentist GWR is made. The performance of variable selection and estimation of the proposed methodology under different circumstances are satisfactory. We further apply the proposed methodology in analysis of a province-level macroeconomic data of thirty selected provinces in China. The estimation and variable selection results reveal insights about China’s economy that are convincing and agree with previous studies and facts.

We introduce a Bayesian spatial-temporal model for analyzing earthquake magnitudes. Specifically, we define a spatial-temporal Pareto regression model with latent multivariate log-Gamma random vectors to analyze earthquake magnitudes. This represents a marked departure from the traditional spatial generalized linear regression model, which uses latent Gaussian random effects. The multivariate log-Gamma distribution results in a full-conditional distribution that can be easily sampled from, which leads to a fast mixing Gibbs sampler. Thus, our proposed model is a computationally efficient approach for modelling Pareto spatial data. The empirical results suggest similar estimation properties between the latent Gaussian model and latent multivariate log-Gamma model, but our proposed model has stronger predictive properties. Additionally, we analyze a small US earthquake data set as an illustration of the effectiveness of our approach.

Spatially resolved transcriptomics technologies enable the measurement of transcriptome information while retaining the spatial context at the regional, cellular or sub-cellular level. While previous computational methods have relied on gene expression information alone for clustering single-cell populations, more recent methods have begun to leverage spatial location and histology information to improve cell clustering and cell-type identification. In this study, using seven semi-synthetic datasets with real spatial locations, simulated gene expression and histology images as well as ground truth cell-type labels, we evaluate 15 clustering methods based on clustering accuracy, robustness to data variation and input parameters, computational efficiency, and software usability. Our analysis demonstrates that even though incorporating the additional spatial and histology information leads to increased accuracy in some datasets, it does not consistently improve clustering compared with using only gene expression data. Our results indicate that for the clustering of spatial transcriptomics data, there are still opportunities to enhance the overall accuracy and robustness by improving information extraction and feature selection from spatial and histology data.

The Cox proportional hazard model is one of the most popular tools in analyzing time-to-event data in public health studies. When outcomes observed in clinical data from different regions yield a varying pattern correlated with location, it is often of great interest to investigate spatially varying effects of covariates. In this paper, we propose a geographically weighted Cox regression model for sparse spatial survival data.In addition, a stochastic neighborhood weighting scheme is introduced at the county level. Theoretical properties of the proposed geographically weighted estimators are examined in detail. A model selection scheme based on the Takeuchi's model robust information criteria (TIC) is discussed. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods. We further apply the proposed methodology to analyze real data on prostate cancer from the Surveillance, Epidemiology, and End Results cancer registry for the state of Louisiana.

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