Variational Prior Replacement in Bayesian Inference and Inversion

Abstract

Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters probabilistically by calculating the posterior probability distribution function. Prior information is often described by a prior probability distribution. Situations arise in which we wish to change prior information during the course of a scientific project. However, estimating the solution to any single Bayesian inference problem is often computationally costly, as it typically requires many model samples to be drawn, and the data set that would have been recorded if each sample was true must be simulated. Recalculating the Bayesian inference solution every time prior information changes can therefore be extremely expensive. We develop a mathematical formulation that allows the prior information that is embedded within a solution, to be changed using variational methods, without recalculating the original Bayesian inference. In this method, existing prior information is removed from a previously obtained posterior distribution and is replaced by new prior information. We therefore call the methodology variational prior replacement (VPR). We demonstrate VPR using a 2D seismic full waveform inversion example, in which VPR provides similar posterior solutions to those obtained by solving independent inference problems using different prior distributions. The former can be completed within minutes on a laptop computer, whereas the latter requires days of computations using high-performance computing resources. We demonstrate the value of the method by comparing the posterior solutions obtained using three different types of prior information: uniform, smoothing and geological prior distributions.

References in corpus (17)

• Variational Inference: A Review for Statisticians
• Normalizing Flows: An Introduction and Review of Current Methods
• Training-image based geostatistical inversion using a spatial generative adversarial neural network
• HypoSVI: Hypocenter inversion with Stein variational inference and Physics Informed Neural Networks
• Seismic tomography using variational inference methods
• 3D Bayesian Variational Full Waveform Inversion
• Probabilistic Neural Network Tomography across Grane field (North Sea) from Surface Wave Dispersion Data
• Probabilistic Neural-Network Based 2D Travel Time Tomography
• An introduction to variational inference in Geophysical inverse problems
• Informed Proposal Monte Carlo
• Variational Bayesian experimental design for geophysical applications: seismic source location, amplitude versus offset inversion, and estimating CO2 saturations in a subsurface reservoir
• Direct multi-modal inversion of geophysical logs using deep learning
• Acoustic Full Waveform Inversion with Hamiltonian Monte Carlo Method
• Introducing Conceptual Geological Information into Bayesian Tomographic Imaging
• Emerging Directions in Geophysical Inversion
• Bayesian Time-Lapse Full Waveform Inversion using Hamiltonian Monte Carlo
• A Tutorial on Parametric Variational Inference

Cited by in corpus (1)

• Power-scaled Bayesian Inference with Score-based Generative Models