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Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
Muography is an imaging tool based on the attenuation of cosmic muons to observe the density distribution of large objects, such as underground caves or fractured zones. Tomography based on muography measurements -- that is, three…
Many geophysical problems can be cast as inverse problems that estimate a set of parameter values from observed data. Within a Bayesian framework, solutions to such problems are described probabilistically by the so-called posterior…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
Seismicity catalogs are larger than ever due to an explosion of techniques for enhanced earthquake detection and an abundance of high-quality datasets. Bayesian inference is an appealing framework for locating earthquakes due to its ability…
Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…
The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has…
Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…
Model misspecification constitutes a major obstacle to reliable inference in many inverse problems. Inverse problems in seismology, for example, are particularly affected by misspecification of wave propagation velocities. In this paper, we…
We present a methodology for quantifying seismic velocity and pore pressure uncertainty that incorporates information regarding the geological history of a basin, rock physics, well log, drilling and seismic data. In particular, our…
The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty due to the noisy data and data scarcity is less discussed in…
Seismic datasets contain valuable information that originate from areas of interest in the subsurface; such seismic reflections are however inevitably contaminated by other events created by waves reverberating in the overburden.…
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…
Accurate seismic imaging and velocity estimation are essential for subsurface characterization. Conventional inversion techniques, such as full-waveform inversion, remain computationally expensive and sensitive to initial velocity models.…
Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…
Travel time tomography for the velocity structure of a medium is a highly non-linear and non-unique inverse problem. Monte Carlo methods are becoming increasingly common choices to provide probabilistic solutions to tomographic problems but…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
The rising number of bridge collapses worldwide has compelled governments to introduce predictive maintenance strategies to extend structural lifespan. In this context, vibration-based Structural Health Monitoring (SHM) techniques utilizing…
Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian…
In anomaly detection (AD), one seeks to identify whether a test sample is abnormal, given a data set of normal samples. A recent and promising approach to AD relies on deep generative models, such as variational autoencoders (VAEs), for…