Data-Driven Forward Discretizations for Bayesian Inversion

A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis

This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches for reliability (rare event probability) analysis of expensive black-box solvers. A naive iteration of these algorithms with respect to different CDF/CCDF threshold values would yield a discretized CDF/CCDF. However, this approach inevitably leads to a trade-off between accuracy…

贝叶斯储层反演的实用高效方法：来自Alvheim油田数据的启示

A practical and efficient approach for Bayesian reservoir inversion: Insights from the Alvheim field data

针对贝叶斯储层反演的计算难题，提出用多元自适应回归样条替代正演模型、结合FFT处理高维场及预条件Crank-Nicolson采样的高效方法，效率提升34倍，经模拟与Alvheim油田数据验证有效。

Structured Bayesian Gaussian process latent variable model: applications to data-driven dimensionality reduction and high-dimensional inversion

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a low-dimensional generative model of the sample-based stochastic prior as well as a surrogate for the forward evaluation. Its Bayesian formulation captures epistemic uncertainty introduced by the limited number of input and output examples, automatically selects an appropriate dimensionality for the learned latent representation of the data, and rigorously propagates…

Dependent Bayesian Lenses: Categories of Bidirectional Markov Kernels with Canonical Bayesian Inversion

We generalise an existing construction of Bayesian Lenses to admit lenses between pairs of objects where the backwards object is dependent on states on the forwards object (interpreted as probability distributions). This gives a natural setting for studying stochastic maps with Bayesian inverses restricted to the points supported by a given prior. In order to state this formally we develop a proposed definition by Fritz of a support object in a Markov category and show that these give rise to a section into the category of dependent Bayesian lenses encoding a more canonical notion of Bayesian …

康普顿成像系统的统计建模与贝叶斯反演：在放射性源定位中的应用

Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localisation

本文提出了一种用于康普顿成像系统的统计正向模型，并在贝叶斯框架下结合Metropolis within Gibbs和期望最大化算法求解逆问题，以估计点状源的位置和能量，相比传统反投影方法提高了准确性并支持不确定性量化。

Cauchy difference priors for edge-preserving Bayesian inversion with an application to X-ray tomography

We study Cauchy-distributed difference priors for edge-preserving Bayesian statistical inverse problems. On the contrary to the well-known total variation priors, one-dimensional Cauchy priors are non-Gaussian priors also in the discretization limit. Cauchy priors have independent and identically distributed increments. One-dimensional Cauchy and Gaussian random walks are special cases of Lévy $α$-stable random walks with $α=1$ and $α=2$, respectively. Both random walks can be written in closed-form, and as priors, they provide smoothing and edge-preserving properties. We briefly discuss also …

数值离散化精度对参数重构与模型参数分布的影响研究

Impact Study of Numerical Discretization Accuracy on Parameter Reconstructions and Model Parameter Distributions

该研究针对光学纳米计量中参数重构的数值离散化精度问题，结合贝叶斯优化、高斯过程代理模型与马尔可夫链蒙特卡洛方法，探究有限元试探函数多项式阶数对重构结果的影响，证实收敛研究可确定高效准确的数值参数。

Sequential pCN-MCMC, an efficient MCMC method for Bayesian inversion of high-dimensional multi-Gaussian priors

In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical inversion are used to condition them on measurement data. Among these techniques, Markov chain Monte Carlo (MCMC) techniques stand out, because they yield asymptotically unbiased conditional realizations. However, standard Markov Chain Monte Carlo (MCMC) methods suffer the curse of dimensionality when refining the discretization. This means that their efficienc…