For strongly non-linear and high-dimensional inverse problems, Markov chain Monte Carlo (MCMC) methods may fail to properly explore the posterior probability density function (PDF) given a realistic computational budget and are generally poorly amenable to parallelization. Particle methods approximate the posterior PDF using the states and weights of a population of evolving particles and they are very well suited to parallelization. We focus on adaptive sequential Monte Carlo (ASMC), an extension of annealed importance sampling (AIS). In AIS and ASMC, importance sampling is performed over a sequence of intermediate distributions, known as power posteriors, linking the prior to the posterior PDF. The AIS and ASMC algorithms also provide estimates of the evidence (marginal likelihood) as needed for Bayesian model selection, at basically no additional cost. ASMC performs better than AIS as it adaptively tunes the tempering schedule and performs resampling of particles when the variance of the particle weights becomes too large. We consider a challenging synthetic groundwater transport inverse problem with a categorical channelized 2D hydraulic conductivity field defined such that the posterior facies distribution includes two distinct modes. The model proposals are obtained by iteratively re-simulating a fraction of the current model using conditional multiple-point statistics (MPS) simulations. We examine how ASMC explores the posterior PDF and compare with results obtained with parallel tempering (PT), a state-of-the-art MCMC inversion approach that runs multiple interacting chains targeting different power posteriors. For a similar computational budget, ASMC outperforms PT as the ASMC-derived models fit the data better and recover the reference likelihood. Moreover, we show that ASMC partly retrieves both posterior modes, while none of them is recovered by PT. Lastly, we demonstrate how the power posteriors obtained by ASMC can be used to assess the influence of the assumed data errors on the posterior means and variances, as well as on the evidence. We suggest that ASMC can advantageously replace MCMC for solving many challenging inverse problems arising in the field of water resources.

对于强非线性和高维逆问题，马尔可夫链蒙特卡罗 (MCMC) 方法可能无法在给定实际计算预算的情况下正确探索后验概率密度函数 (PDF)，并且通常不太适合并行化。粒子方法使用一组进化粒子的状态和权重来近似后验概率密度函数，它们非常适合并行化。我们专注于自适应顺序蒙特卡罗 (ASMC)，它是退火重要性采样 (AIS) 的扩展。在 AIS 和 ASMC 中，重要性采样是在一系列中间分布（称为幂后验）上执行的，将先验与后验 PDF 联系起来。AIS 和 ASMC 算法还提供贝叶斯模型选择所需的证据估计（边际似然），基本上没有额外费用。ASMC 比 AIS 表现更好，因为它自适应地调整回火计划并在粒子权重的方差变得太大时执行粒子重采样。我们考虑了一个具有挑战性的合成地下水输送逆问题，其中定义了分类通道化的二维水力传导率场，使得后相分布包括两种不同的模式。模型建议是通过使用条件多点统计 (MPS) 模拟迭代地重新模拟当前模型的一部分来获得的。我们研究了 ASMC 如何探索后验概率密度函数，并与使用并行回火 (PT) 获得的结果进行比较，这是一种最先进的 MCMC 反演方法，运行针对不同功率后验的多个相互作用链。对于类似的计算预算，ASMC 优于 PT，因为 ASMC 派生的模型更好地拟合数据并恢复参考可能性。此外，我们表明 ASMC 部分检索了两种后验模式，而 PT 没有恢复它们。最后，我们展示了如何使用 ASMC 获得的功率后验来评估假设数据误差对后验均值和方差以及证据的影响。我们建议 ASMC 可以有利地替代 MCMC，以解决水资源领域出现的许多具有挑战性的逆问题。我们展示了如何使用 ASMC 获得的功率后验来评估假设数据误差对后验均值和方差以及证据的影响。我们建议 ASMC 可以有利地替代 MCMC，以解决水资源领域出现的许多具有挑战性的逆问题。我们展示了如何使用 ASMC 获得的功率后验来评估假设数据误差对后验均值和方差以及证据的影响。我们建议 ASMC 可以有利地替代 MCMC，以解决水资源领域出现的许多具有挑战性的逆问题。