通过可调幂参数实现贝叶斯推断中先验与似然的灵活控制，提升地震速度模型生成质量。
Power-scaled Bayesian Inference with Score-based Generative Models
- 引入幂尺度评分生成算法，实现先验与似然的动态调节而无需重训练。
- 提高似然幂值可增强样本对地震成像数据的拟合度，降低震源残差。
- 降低先验幂值能增加样本结构多样性，适用于敏感性分析与不确定性量化。
我们提出一种基于评分的生成算法，用于在贝叶斯推断框架下从幂尺度化的先验和似然中采样。该算法可在不重新训练的情况下，灵活调控先验与似然的影响权重。重点应用于基于地震成像数据生成地震速度模型。通过采样中间幂后验分布，实现敏感性分析，评估先验与似然对后验样本的相对影响。在多种设置下测试不同幂参数的效果：仅作用于先验、仅作用于似然，或同时作用于两者。结果表明，将似然幂值提升至某一阈值内可显著提高后验样本对条件数据（如地震图像）的保真度；降低先验幂值则促进样本间结构多样性。此外，适度放大似然幂值可有效降低射线数据残差，验证其在后验精化中的有效性。
原文摘要 · Abstract (English)
We propose a score-based generative algorithm for sampling from power-scaled priors and likelihoods within the Bayesian inference framework. Our algorithm enables flexible control over prior-likelihood influence without requiring retraining for different power-scaling configurations. Specifically, we focus on synthesizing seismic velocity models conditioned on imaged seismic. Our method enables sensitivity analysis by sampling from intermediate power posteriors, allowing us to assess the relative influence of the prior and likelihood on samples of the posterior distribution. Through a comprehensive set of experiments, we evaluate the effects of varying the power parameter in different settings: applying it solely to the prior, to the likelihood of a Bayesian formulation, and to both simultaneously. The results show that increasing the power of the likelihood up to a certain threshold improves the fidelity of posterior samples to the conditioning data (e.g., seismic images), while decreasing the prior power promotes greater structural diversity among samples. Moreover, we find that moderate scaling of the likelihood leads to a reduced shot data residual, confirming its utility in posterior refinement.
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