用贝叶斯方法评估影像生物标志物的可重复性，助力精准治疗响应分析。

The assessment of imaging biomarkers is critical for advancing precision medicine and improving disease characterization. Despite the availability of methods to derive disease heterogeneity metrics in imaging studies, a robust framework for evaluating measurement uncertainty remains underdeveloped. To address this gap, we propose a novel Bayesian framework to assess the precision of disease heterogeneity measures in biomarker studies. Our approach extends traditional methods for evaluating biomarker precision by providing greater flexibility in statistical assumptions and enabling the analysis of biomarkers beyond univariate or multivariate normally-distributed variables. Using Hamiltonian Monte Carlo sampling, the framework supports both, for example, normally-distributed and Dirichlet-Multinomial distributed variables, enabling the derivation of posterior distributions for biomarker parameters under diverse model assumptions. Designed to be broadly applicable across various imaging modalities and biomarker types, the framework builds a foundation for generalizing reproducible and objective biomarker evaluation. To demonstrate utility, we apply the framework to whole-body diffusion-weighted MRI (WBDWI) to assess heterogeneous therapeutic responses in metastatic bone disease. Specifically, we analyze data from two patient studies investigating treatments for metastatic castrate-resistant prostate cancer (mCRPC). Our results reveal an approximately 70% response rate among individual tumors across both studies, objectively characterizing differential responses to systemic therapies and validating the clinical relevance of the proposed methodology. This Bayesian framework provides a powerful tool for advancing biomarker research across diverse imaging-based studies while offering valuable insights into specific clinical applications, such as mCRPC treatment response.