An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems

Abstract

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation. However, in many practical problems, the parameter of interest can be of high dimensionality, which renders standard model reduction techniques infeasible. In this paper, we present an approach that employs the ANOVA decomposition method to reduce the model with respect to the unknown parameters, and the reduced basis method to reduce the model with respect to the physical parameters. Moreover, we provide an adaptive scheme within the MCMC iterations, to perform the ANOVA decomposition with respect to the posterior distribution. With numerical examples, we demonstrate that the proposed model reduction method can significantly reduce the computational cost of Bayesian inverse problems, without sacrificing much accuracy.

Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems

“…( 4) must be computed numerically. To this end, MCMC [10,44] or other approximation methods like Ensemble Kalman filter (EnKF) [16,30] are often employed. However, there are still two main difficulties for these methods.…”

“…For the first problem identified above, given prior information, parameterization methods are often used to provide a low-dimensional embedding of the unknown spatially-varying parameter. The common method in BIPs is the truncated Karhunen-Loève expansion (KLE) for the estimation of Gaussian random fields (GRFs) [10,11], where inference is performed over a small number of expansion coefficients. With limitations and strong assumptions on the mean and covariance functions, the KLE cannot reflect the true prior information, and is not a good choice for fields with nontrivial correlation structure.…”

“…. , L), explore the posterior distribution p(z l |D obs ) in Eq (10). recursively from coarse-to fine-scales by using MCMC or other posterior modeling techniques.…”

Analisis Statisik Perbandingan Manipulasi Suara Dan Suara Asli Menggunakan Teknik Audio Forensik

“…Dalam makalah ini akan membandingkan nilai Picth, Formant, dan Bandwith antara suara barang bukti (unknown) dengan suara pembanding (known) dengan menggunakan tool audio forensik, dan menggunakan beberapa fitur didalamnya [6]. Analisa One Way Annova [7], [8], [9] dilakukan untuk menunjukkan identik atau tidaknya dua kelompok suara dari masingmasing formant antara suara unknown dan known. Pada akhirnya akan diperoleh kesimpulan dari dua suara sumber tersebut apakah dinyatakan identik atau tidak identik sebagai gambaran untuk pembuktian di pengadilan jika tim forensik mengalami kasus serupa [10], [11].…”

Bayesian Approach to Inverse Time-harmonic Acoustic Scattering from Sound-soft Obstacles with Phaseless Data

“…Besides, the surrogate model also characterizes the posterior distribution, since the snapshots of the reduced-order model are adaptively calculated from the posterior distribution during the iterations of MCMC method. Liao and Li [23] proposed the Analysis of Variance (ANOVA) method to reduce the forward model both in the statistical space and in the physical space. The reduced basis ANOVA model with respect to the posterior distribution is then used in the MCMC iterations by an adaptive scheme.…”