Bayesian Modeling of Spatial Transcriptomics Data via a Modified Ising Model

Recent technology breakthroughs in spatial molecular profiling (SMP), such as spatial transcriptomics sequencing, have enabled the comprehensive molecular characterization of single cells while preserving spatial and morphological information. One immediate question is how to identify spatially variable (SV) genes. Most of the current work builds upon the geostatistical model with Gaussian process that relies on the selection of \textit{ad hoc} kernels to account for spatial expression patterns. To overcome this potential challenge and capture more spatial patterns, we introduced a Bayesian modeling framework to identify SV genes. Our model first dichotomized the complex sequencing count data into latent binary gene expression levels. Then, binary pattern quantification problem is considered as a spatial correlation estimation problem via a modified Ising model using Hamiltonian energy to characterize spatial patterns. We used auxiliary variable Markov chain Monte Carlo algorithms to sample from the posterior distribution with an intractable normalizing constant. Simulation results showed high accuracy in detecting SV genes compared with kernel-based alternatives. We also applied our model to two real datasets and discovered novel spatial patterns that shed light on the biological mechanisms. This statistical methodology presents a new perspective for characterizing spatial patterns from SMP data.