A variational Bayesian approach for inverse problems with skew-t error distributions
A variational Bayesian approach for inverse problems with skew-t error distributions
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DOI：
10.1016/j.jcp.2015.07.062
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发表时间：
2015-11
期刊：
影响因子：
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通讯作者：
Nilabja Guha;Xiaoqing Wu;Y. Efendiev;Bangti Jin;B. Mallick
中科院分区：
文献类型：
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作者：
Nilabja Guha;Xiaoqing Wu;Y. Efendiev;Bangti Jin;B. Mallick
在这项工作中，我们开发了一种新颖的稳健贝叶斯方法来解决偏态分布后的数据错误问题。在反问题设置中开发了分层贝叶斯模型。贝叶斯方法包含先验分布形式的自然正则化机制，并且使用 LASSO 类型先验分布来强烈诱导稀疏性。我们通过最小化真实后验分布和可分离近似之间的 Kullback-Leibler 散度，提出了一种变分类型算法。所提出的方法在几个二维线性和非线性反问题上进行了说明，例如柯西问题和渗透率估计问题。
In this work, we develop a novel robust Bayesian approach to inverse problems with data errors following a skew-tdistribution. A hierarchical Bayesian model is developed in the inverse problem setup. The Bayesian approach contains a natural mechanism for regularization in the form of a prior distribution, and a LASSO type prior distribution is used to strongly induce sparseness. We propose a variational type algorithm by minimizing the Kullback–Leibler divergence between the true posterior distribution and a separable approximation. The proposed method is illustrated on several two-dimensional linear and nonlinear inverse problems, e.g. Cauchy problem and permeability estimation problem.