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Bayesian inference for inverse problems involves computing expectations under posterior distributions -- e.g., posterior means, variances, or predictive quantities -- typically via Monte Carlo (MC) estimation. When the quantity of interest…
The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…
We investigate the convergence rates of variational posterior distributions for statistical inverse problems involving nonlinear partial differential equations (PDEs). Departing from exact Bayesian inference, variational inference…
The COVID-19 pandemic provides new motivation for a classic problem in epidemiology: estimating the empirical rate of transmission during an outbreak (formally, the time-varying reproduction number) from case counts. While standard methods…
We propose a novel particle-based variational inference method designed to work with multimodal distributions. Our approach, referred to as Branched Stein Variational Gradient Descent (BSVGD), extends the classical Stein Variational…
In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…
Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however,…
The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…
Full waveform inversion is an ill-posed inverse problem whose solution non-uniqueness -- i.e., arising from band-limited, finite-aperture, noisy data -- calls for uncertainty quantification to avoid overconfident geological interpretations.…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
We consider situations in Bayesian analysis where we have a family of priors $\nu_h$ on the parameter $\theta$, where $h$ varies continuously over a space $\mathcal{H}$, and we deal with two related problems. The first involves sensitivity…
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
The curse of dimensionality is a longstanding challenge in Bayesian inference in high dimensions. In this work, we propose a projected Stein variational gradient descent (pSVGD) method to overcome this challenge by exploiting the…
Bayesian computation plays an important role in modern machine learning and statistics to reason about uncertainty. A key computational challenge in Bayesian inference is to develop efficient techniques to approximate, or draw samples from…
Stein Variational Gradient Descent (SVGD) is a highly efficient method to sample from an unnormalized probability distribution. However, the SVGD update relies on gradients of the log-density, which may not always be available. Existing…
Bayesian inference for high-dimensional inverse problems is computationally costly and requires selecting a suitable prior distribution. Amortized variational inference addresses these challenges via a neural network that approximates the…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
Discrete state spaces represent a major computational challenge to statistical inference, since the computation of normalisation constants requires summation over large or possibly infinite sets, which can be impractical. This paper…