自适应序贯蒙特卡罗方法在复杂地质先验模型选择和后验推断中的应用
Adaptive sequential Monte Carlo for posterior inference and model selection among complex geological priors
摘要：
贝叶斯模型选择，使空间先验模型描述的概念地下模型的比较和排名，根据可用的地球物理数据提供的支持。深度生成神经网络可以有效地编码这种复杂的空间先验，从而允许以增强的非线性为代价的强大模型降维。在这种情况下，我们探索了最近的自适应序贯蒙特卡罗（ASMC）方法，该方法建立在退火重要性抽样（AIS）的基础上;该方法通过粒子近似提供后验概率密度函数（PDF）和证据（贝叶斯模型选择的中心量）。这两种技术都非常适合并行计算，并依赖于重要性采样的中间分布的序列，连接先验和后验PDF。每个后续的分布近似更新粒子的权重和状态，与以前的近似相比，使用一个小的预定义数量的马尔可夫链蒙特卡罗（MCMC）的建议步骤。与AIS相比，ASMC方法自适应地调整相邻分布之间的调和，并在粒子权值方差过大时执行粒子的重新排序。我们评估ASMC使用两种不同的概念模型和相关的合成跨孔探地雷达（GPR）层析成像数据。对于最具挑战性的测试情况下，我们发现，ASMC方法是更快，更可靠的定位后PDF比国家的最先进的自适应MCMC。证据估计被认为是强大的ASMC算法变量的选择和更不敏感的模型建议类型比MCMC。[...]
英文摘要：
Bayesian model selection enables comparison and ranking of conceptual subsurface models described by spatial prior models, according to the support provided by available geophysical data. Deep generative neural networks can efficiently encode such complex spatial priors, thereby, allowing for a strong model dimensionality reduction that comes at the price of enhanced non-linearity. In this setting, we explore a recent adaptive sequential Monte Carlo (ASMC) approach that builds on Annealed Importance Sampling (AIS); a method that provides both the posterior probability density function (PDF) and the evidence (a central quantity for Bayesian model selection) through a particle approximation. Both techniques are well suited to parallel computation and rely on importance sampling over a sequence of intermediate distributions, linking the prior and the posterior PDF. Each subsequent distribution is approximated by updating the particle weights and states, compared with the previous approximation, using a small pre-defined number of Markov chain Monte Carlo (MCMC) proposal steps. Compared with AIS, the ASMC method adaptively tunes the tempering between neighboring distributions and performs resampling of particles when the variance of the particle weights becomes too large. We evaluate ASMC using two different conceptual models and associated synthetic cross-hole ground penetrating radar (GPR) tomography data. For the most challenging test case, we find that the ASMC method is faster and more reliable in locating the posterior PDF than state-of-the-art adaptive MCMC. The evidence estimates are found to be robust with respect to the choice of ASMC algorithmic variables and much less sensitive to the model proposal type than MCMC.[...]
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