  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.
