论文标题
贝叶斯逆问题使用同义
Bayesian inverse problems using homotopy
论文作者
论文摘要
在解决贝叶斯逆问题时，通常希望使用共同的密度参数化表示先验和后部。通常，我们寻求与先前同一家族的密度，该密度紧密近似真正的后部。作为统计中最重要的分布类别之一，指数族被视为参数化。通过最小化参数化密度与同型在后部密度变形的参数密度和同质性之间的偏差来实现代表近似后验的最佳参数值。它没有试图解决原始问题，而是将其完全转换为相应的显式普通一阶微分方程的系统。通过有限的“时间”间隔求解该系统可产生所需的最佳密度参数。通过一些数值示例，该方法被证明是有效的。
In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true posterior. As one of the most important classes of distributions in statistics, the exponential family is considered as the parameterization. The optimal parameter values for representing the approximated posterior are achieved by minimizing the deviation between the parameterized density and a homotopy that deforms the prior density into the posterior density. Rather than trying to solve the original problem, it is exactly converted into a corresponding system of explicit ordinary first-order differential equations. Solving this system over a finite 'time' interval yields the desired optimal density parameters. This method is proven to be effective by some numerical examples.
