论文标题
非线性正向模型的随机变异贝叶斯推断
Stochastic Variational Bayesian Inference for a Nonlinear Forward Model
论文作者
论文摘要
在贝叶斯推断非线性模型参数的背景下，变异贝叶斯（VB）已用于促进后验分布的计算。以前，已经为非线性模型推断了具有加斯高斯噪声的数据的非线性模型推断Vb的分析公式，以替代非线性最小二乘。这里得出了一个随机解决方案，该解决方案避免了分析公式所需的一些近似值，提供了可以在非线性模型推理问题上更灵活地部署的解决方案。随机VB溶液用于推断Biexponential玩具案例和探索算法参数空间，然后在磁共振成像研究中部署在灌注研究中的真实数据之前。发现新方法可以实现可比较的参数恢复与分析解决方案，尽管依赖于抽样，但在计算速度方面具有竞争力。
Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been derived for nonlinear model inference on data with additive gaussian noise as an alternative to nonlinear least squares. Here a stochastic solution is derived that avoids some of the approximations required of the analytical formulation, offering a solution that can be more flexibly deployed for nonlinear model inference problems. The stochastic VB solution was used for inference on a biexponential toy case and the algorithmic parameter space explored, before being deployed on real data from a magnetic resonance imaging study of perfusion. The new method was found to achieve comparable parameter recovery to the analytic solution and be competitive in terms of computational speed despite being reliant on sampling.
