Related papers: Summary statistics from training images as prior i…
The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator. From a Bayesian perspective, changes from the prior to the…
Bayesian aggregation lets election forecasters combine diverse sources of information, such as state polls and economic and political indicators: as in our collaboration with The Economist magazine. However, the demands of real-time…
Reconstructing the structural geology and mineral composition of the first few kilometers of the Earth's subsurface from sparse or indirect surface observations remains a long-standing challenge with critical applications in mineral…
To obtain high-resolution images of subsurface structures from seismic data, seismic imaging techniques such as Full Waveform Inversion (FWI) serve as crucial tools. However, FWI involves solving a nonlinear and often non-unique inverse…
Structural seismic interpretation and quantitative characterization are historically intertwined processes. The latter provides estimates of properties of the subsurface which can be used to aid structural interpretation alongside the…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a…
Accurately characterizing migration velocity models is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional velocity model building methods such as…
Efficient assessment of convolved hidden Markov models is discussed. The bottom-layer is defined as an unobservable categorical first-order Markov chain, while the middle-layer is assumed to be a Gaussian spatial variable conditional on the…
State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…
The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem.…
Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…
Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a…
Groundwater flow modeling is commonly used to calculate groundwater heads, estimate groundwater flow paths and travel times, and provide insights into solute transport processes within an aquifer. However, the values of input parameters…
Bayesian geoacoustic inversion problems are conventionally solved by Markov chain Monte Carlo methods or its variants, which are computationally expensive. This paper extends the classic Bayesian geoacoustic inversion framework by deriving…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
Full waveform inversion (FWI) is an advanced seismic inversion technique for quantitatively estimating subsurface properties. However, with FWI, it is hard to converge to a geologically-realistic subsurface model. Thus, we propose a…
We present a way to capture high-information posteriors from training sets that are sparsely sampled over the parameter space for robust simulation-based inference. In physical inference problems, we can often apply domain knowledge to…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…