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The location, timing, and abundance of gene expression (both mRNA and proteins) within a tissue define the molecular mechanisms of cell functions. Recent technology breakthroughs in spatial molecular profiling, including imaging-based technologies and sequencing-based technologies, have enabled the comprehensive molecular characterization of single cells while preserving their spatial and morphological contexts. This new bioinformatics scenario calls for effective and robust computational methods to identify genes with spatial patterns. We represent a novel Bayesian hierarchical model to analyze spatial transcriptomics data, with several unique characteristics. It models the zero-inflated and over-dispersed counts by deploying a zero-inflated negative binomial model that greatly increases model stability and robustness. Besides, the Bayesian inference framework allows us to borrow strength in parameter estimation in a de novo fashion. As a result, the proposed model shows competitive performances in accuracy and robustness over existing methods in both simulation studies and two real data applications. The related R/C++ source code is available at https://github.com/Minzhe/BOOST-GP.