Power-scaled Bayesian Inference with Score-based Generative Models
This work addresses the need for flexible sensitivity analysis in Bayesian inference for domain-specific applications like seismic imaging, though it appears incremental as it adapts existing score-based methods to power-scaling.
The paper tackles the problem of controlling prior-likelihood influence in Bayesian inference for seismic velocity modeling, proposing a score-based generative algorithm that samples from power-scaled priors and likelihoods without retraining. Results show that increasing likelihood power improves fidelity to conditioning data (e.g., seismic images) up to a threshold, while decreasing prior power enhances structural diversity, with moderate scaling reducing shot data residual.
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.