SIAM Journal on Scientific Computing, Volume 43, Issue 2, Page A1062-A1080, January 2021.
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling method by constructing new indicator functions to obtain the approximate locations of the sources. The behavior of the indicators is analyzed. Second, the inverse problem is formulated as a statistical inference problem using the Bayes' formula. The well-posedness of the posterior distribution is proved. The source locations obtained in the first step are coded in the priors. Then a Metropolis--Hastings Markov chain Monte Carlo algorithm is used to explore the posterior density. Both steps use the same physical model and measured data. Numerical experiments show that the proposed method using partial data is effective.

中文翻译：

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具有部分数据的声源反问题的质量贝叶斯方法

SIAM科学计算杂志，第43卷，第2期，第A1062-A1080页，2021年1月。
提出了一种将直接采样方法与贝叶斯反演相结合的质量贝叶斯方法，以利用部分数据重建未知声源的位置和强度。首先，我们通过构造新的指标函数来扩展直接采样方法，以获得源的近似位置。分析指标的行为。其次，使用贝叶斯公式将反问题表述为统计推断问题。证明了后验分布的适定性。第一步中获得的源位置先验编码。然后使用Metropolis-Hastings马尔可夫链蒙特卡罗算法来探索后验密度。这两个步骤使用相同的物理模型和测量数据。