  Identifying genes that display spatial patterns is critical to investigating
expression interactions within a spatial context and further dissecting
biological understanding of complex mechanistic functionality. Despite the
increase in statistical methods designed to identify spatially variable genes,
they are mostly based on marginal analysis and share the limitation that the
dependence (network) structures among genes are not well accommodated, where a
biological process usually involves changes in multiple genes that interact in
a complex network. Moreover, the latent cellular composition within spots may
introduce confounding variations, negatively affecting identification accuracy.
In this study, we develop a novel Bayesian regularization approach for spatial
transcriptomic data, with the confounding variations induced by varying
cellular distributions effectively corrected. Significantly advancing from the
existing studies, a thresholded graph Laplacian regularization is proposed to
simultaneously identify spatially variable genes and accommodate the network
structure among genes. The proposed method is based on a zero-inflated negative
binomial distribution, effectively accommodating the count nature, zero
inflation, and overdispersion of spatial transcriptomic data. Extensive
simulations and the application to real data demonstrate the competitive
performance of the proposed method.
