论文标题
贝叶斯推断预计密度
Bayesian Inference with Projected Densities
论文作者
论文摘要
约束是贝叶斯推论中先前信息的自然选择。在各种应用中，感兴趣的参数位于约束集的边界上。在本文中，我们使用一种隐式定义约束先验的方法，以使后验分配给约束集的边界的正概率。我们表明，通过将后质量投射到约束集上，我们在该集合的边界上获得了一个具有丰富概率结构的新后部。如果原始后验是高斯人，则可以有效地进行这样的投影。我们将方法应用于贝叶斯线性反问题，在这种情况下，可以通过反复求解约束最小二乘问题的问题，类似于MAP估计，但数据中有扰动。当组合成贝叶斯分层模型和约束集是一个多面体锥时，我们可以得出Gibbs采样器以有效地从分层模型中采样。为了显示投射后验的效果，我们将该方法应用于脱毛和计算机断层扫描示例。
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a constrained prior such that the posterior assigns positive probability to the boundary of the constraint set. We show that by projecting posterior mass onto the constraint set, we obtain a new posterior with a rich probabilistic structure on the boundary of that set. If the original posterior is a Gaussian, then such a projection can be done efficiently. We apply the method to Bayesian linear inverse problems, in which case samples can be obtained by repeatedly solving constrained least squares problems, similar to a MAP estimate, but with perturbations in the data. When combined into a Bayesian hierarchical model and the constraint set is a polyhedral cone, we can derive a Gibbs sampler to efficiently sample from the hierarchical model. To show the effect of projecting the posterior, we applied the method to deblurring and computed tomography examples.
